A Novel Approach for the Optimization of Segmental Linings in TBM Tunnels through Steel Ring Reinforcement

A Novel Approach for the Optimization of Segmental Linings in TBM Tunnels through Steel Ring Reinforcement | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A Novel Approach for the Optimization of Segmental Linings in TBM Tunnels through Steel Ring Reinforcement Cemre Çağlar, Berna Unutmaz, Candan Gökçeoğlu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8554968/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The escalating demands of global urbanization necessitate efficient and robust underground construction methods, with Tunnel Boring Machines (TBMs) being the predominant choice. The long-term performance of these projects heavily relies on the efficacy and structural reliability of precast concrete segmental lining systems. Despite their advantages, these linings are susceptible to critical structural weaknesses, such as high stress concentrations at joints and excessive deformations in challenging ground conditions. While reducing segment thickness offers sufficient economic and environmental benefits (material saving and reduced excavation diameter), it inherently compromises structural stiffness and safety margins. This study investigates the potential of internal steel rings as a supplementary reinforcement strategy to enhance the mechanical performance of thinner segmental linings, drawing conceptual inspiration from the successful application of steel support systems in the New Austrian Tunnelling Method (NATM). A comprehensive numerical comparative analysis was conducted using the PLAXIS 3D Finite Element Method under challenging rock mass and high overburden conditions. Three distinct tunnel lining models were simulated: a 25 cm reinforced concrete segment lining (Model 1), a 40 cm reinforced segment lining (Model 2), and a 25 cm reinforced concrete segment lining with strategically placed steel rings (Model 3). The analysis focused on Key Performance Indicators (KPIs), including total deformation, N 2 axial forces, Q 12 shear forces, and M 11 bending moments, and validated the structural safety using N-M interaction curves. The results demonstrate that the integration of steel rings successfully promotes a more favourable redistribution of internal forces, significantly reducing the critical bending moment M 11 demands on the concrete segments. Crucially, the numerical findings confirm that thinner 25 cm segments, when supported with steel rings, achieve structural performance levels comparable to, or even superior to, conventional thicker 40 cm segments, while maintaining a substantial safety margin as verified by the N-M interaction diagrams. This research validates a structurally robust and logistically efficient approach for material optimization, offering considerable potential for both economic and structural improvements in TBM tunnel design and aligning strongly with sustainable construction principles. Physical sciences/Engineering Physical sciences/Materials science Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 1. Introduction The rising demands of global urbanization and the ongoing necessity for strong infrastructure have established Mechanized Tunnelling, mainly using Tunnel Boring Machines (TBMs), as the most effective approach for constructing underground facilities in heavily populated urban areas and challenging geological conditions [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ]. The effective implementation and sustained performance of these projects are primarily reliant on the structural effectiveness of precast concrete segmental linings [ 7 ], [ 8 ], [ 9 ], [ 10 ]. These linings act as the main structural support, withstanding intricate geotechnical loads and ensuring tunnel stability. Precast concrete segments are widely employed because of their quick installation, excellent compressive strength, and modular design, enabling accurate and controlled assembly as the tunnel progresses [ 8 ], [ 11 ], [ 12 ], [ 13 ]. These components are required to resist a complex set of loads, such as radial ground pressures, bending moments, and axial forces that are transferred through the interconnected tunnel ring system [ 14 ], [ 15 ], [ 16 ], [ 17 ]. Despite their many benefits, TBM segmental linings also present certain structural challenges. A major issue is the formation of high stress concentrations, commonly occurring at the joints between segments, which act as critical zones of structural vulnerability [ 18 ], [ 19 ], [ 20 ]. Moreover, in difficult geological conditions—such as squeezing ground, highly deformable soft clays, or zones with considerable ground relaxation—segmental linings may undergo excessive deformation, which can adversely affect their long-term stability and structural integrity [ 21 ], [ 22 ], [ 23 ]. This challenge is further intensified by uncertainties associated with insufficient in-situ geotechnical information. Such gaps can result in overly conservative designs—leading to unnecessary material use and higher costs—or, more critically, under-designed systems that introduce significant structural and safety risks [ 3 ], [ 24 ], [ 25 ], [ 26 ]. To reduce material usage and construction costs while improving structural performance, various alternative approaches have been investigated, such as employing high-performance concrete or implementing prestressed lining systems [ 22 ], [ 27 ], [ 28 ], [ 29 ]. Although successful in certain applications, these approaches often add construction complexity or rely on costly specialized materials, which can diminish the expected benefits. Consequently, finding a practical and efficient way to enhance the mechanical performance of thinner segments continues to be an important research challenge [ 13 ], [ 21 ], [ 27 ]. TBM linings resist ground pressures through axial compression and flexural resistance [ 30 ], [ 31 ], [ 32 ], [ 33 ], [ 34 ], though segment joints often create stress concentrations that risk structural damage [ 8 ], [ 16 ], [ 17 ], [ 35 ], [ 36 ]. While reducing segment thickness offers economic and environmental benefits by decreasing volume of excavation, it significantly lowers lining stiffness and increases vulnerability to deformation [ 12 ], [ 13 ], [ 17 ], [ 29 ], [ 31 ], [ 37 ], [ 38 ]. Inspired by the efficacy of steel arches in NATM [ 24 ], [ 33 ], [ 39 ], [ 40 ], [ 41 ], this study explores internal steel rings to maintain stability in thinner TBM segments. Despite the prevalence of numerical modeling in tunnel engineering [ 23 ], [ 31 ], [ 42 ], [ 43 ], [ 44 ], a research gap exists in quantifying the specific impact of steel rings on TBM lining performance. This study is therefore specifically designed to bridge this identified critical research gap. By performing a rigorous numerical comparative analysis using PLAXIS 3D, we evaluated the structural performance across three distinct model configurations: (1) 25 cm thin segments without reinforcement, (2) reference 40 cm thick segments without reinforcement, and (3) 25 cm thin segments strategically reinforced with steel rings. The analysis focuses on key performance indicators, including total displacement, the distribution patterns of axial (N2) and shear forces (Q12), and critical bending moments (M11), with the goal of definitively ascertaining whether this integrated system can reliably achieve superior structural performance while allowing for substantial material optimization. This approach aligns with the broader objective of achieving performance-based optimization for future TBM-driven tunneling projects. 2. Methodology 2.1. Numerical Modelling Software and Approach For the numerical modelling in this study, the PLAXIS 3D software was utilized (Potts & Zdravkovid, 1999; Sakil Ahmed et al., 2023). The dimensions of the numerical models were carefully determined to be sufficiently large, thereby encompassing the full influence zone of the tunnel excavation within the surrounding ground. Consequently, for all three distinct tunnel models investigated, the overall dimensions were consistently set at 25 m (width) x 85 m (depth) x 100 m (length). The tunnel excavation process was specifically modelled to advance along the Y-axis of the coordinate system. Due to the inherent symmetrical nature of the tunnel structure, which implies symmetrical distributions of resulting deformations and stresses, modelling only the left half of the tunnel was sufficient for obtaining accurate and representative results. 2.2. Ground Conditions and Material Properties An idealized, homogeneous ground profile was defined for the analysis. To create a representative and challenging scenario for the tunnel-ground interaction, the profile was simplified to a single, deep layer of Claystone. The tunnel axis was placed at an elevation of -11.25 m, which resulted in a significant overburden depth of 71.25 m from the ground surface (see Fig. 1 ). The groundwater table was positioned at the 0.00 m to ensure saturated conditions around the tunnel and to contribute to the high-stress environment. The Hoek-Brown material model was chosen to accurately simulate the non-linear behaviour of the rock mass under stress. The specific parameters for the Claystone are presented in Table 1 . Table 1 Rock mass parameters of Claystone employed in the study Parameter Value Unit Elevation Range + 60.0 m to -25.0 m - Uniaxial Compressive Strength (intact rock), σci​ 20 MPa Geological Strength Index (GSI) 25 - Material Constant (intact rock), mi​ 5 - Disturbance Factor, D 0.8 - Unit Weight, γ 23 kN/m³ Rock Mass Deformation Modulus, Erm​ 1.5 GPa Poisson's Ratio, ν 0.3 - To allow for a more robust comparison of axial loads, shear forces, and moments within the reinforced concrete lining material in the analyses, parameters reflecting linear elastic material behaviour suitable for shell elements were adopted. The specific properties for the concrete lining, which were defined for plate elements in PLAXIS 3D, are detailed in Table 2 . Representing lining elements as continuum soil elements was avoided in PLAXIS 3D to facilitate the direct extraction and comparison of internal structural forces (axial loads, shear forces, and bending moments) from such units. Reinforcement placement of the concrete segments is shown in Fig. 2 for both 25 cm and 40 cm thick segments. Table 2 Linear Elastic Parameters for Concrete Segmental Linings Parameter Value Unit Thickness (d) 0.25 or 0.40 (variable) m Unit Weight, γ 24 kN/m³ Material Model Linear Elastic - Isotropic Yes - Young's Modulus, E 30 GPa Poisson's Ratio, ν 0.20 - The steel ring elements, which constitute a central focus of this study, were defined as a linear elastic material model and represented as shell elements. For Model 3 (25 cm segments with rings), the thickness of these elements was set at 0.25 m. The specific material properties used for the steel rings are detailed in Table 3 . A perfect bond was assumed between the steel rings and the concrete segments in the numerical model, implying full composite action and ensuring the structural integrity of the tunnel body. These steel elements, similar to reinforced concrete segments, were modelled to be assembled in sections within the tunnel to form a circular shape conforming to the tunnel geometry. The cross section of the steel ring and complete ring structure from tunnel cross section are shown in Fig. 3 . Table 3 Linear Elastic Parameters for Steel Rings Parameter Value Unit Thickness (d) 0.25 m Unit Weight, γ 78.50 kN/m³ Material Model Linear Elastic - Isotropic Yes - Young's Modulus, E 210 GPa Poisson's Ratio, ν 0.30 - A simplified representation of the TBM shield body was incorporated into the numerical model. This TBM body was defined using plate elements with linear elastic material properties, designed to symbolize the presence and effect of the advancing machine within the excavation. The specific parameters utilized for the TBM shield are presented in Table 4 . Notably, the unit weight of 247 kN/m³ was adopted for the TBM shield, consistent with recommendations found in the PLAXIS 3D manual [ 45 ]. Table 4 Linear Elastic Parameters for the TBM Shield Body Parameter Value Unit Thickness (d) 0.17 m Unit Weight, γ 247 kN/m³ Material Model Linear Elastic - Isotropic Yes - Young's Modulus, E 200 GPa Poisson's Ratio, ν 0.00 - The 3D and profile views of the model are shown in Fig. 4 and Fig. 5 , respectively. 2.3. Geometric Model and Discretization The internal diameter of the tunnel was set at 8 meters for each individual model configuration. For sections with a segment thickness of 25 cm, the external tunnel diameter was 8.50 m, while for section with a segment thickness of 40 cm, the external tunnel diameter was 8.80 m. The total length of the modelled tunnel section was defined to minimize boundary effects. The depth of the tunnel axis from the ground surface was 71.25 m. The tunnel lining segments were modelled as rectangular-section segments, curving to conform to the tunnel's circular geometry. Each segment possessed a constant width of 1.5 m in the longitudinal direction of the tunnel axis, corresponding to a single excavation step of 1.5 m during the tunnel advancement simulation. The segment thicknesses varied according to the specific model configuration: Model 1: 25 cm thick concrete segments without steel rings. Model 2: 40 cm thick concrete segments without steel rings. Model 3: 25 cm thick concrete segments with strategically placed steel rings. The internal steel rings were designed with a solid rectangular cross-section. Initial trials considered a ring width of 0.20 m; however, based on preliminary assessments of efficiency, a width of 0.25 m was ultimately adopted for these rings, which were positioned along the tunnel axis. Regarding longitudinal placement, while an initial consideration involved installing steel rings every five concrete segments, leading to a 7.5 m spacing, this interval was deemed too large. Consequently, a more accurate and effective placement strategy was chosen, involving the installation of steel rings every three concrete segments along the tunnel's longitudinal direction, resulting in a consistent spacing of 4.5 m (3 segments x 1.5 m/segment). These steel rings were also represented using shell elements in the numerical model. For the models 1 and 2, the steel rings are geometrically placed as in the model 3. The primary distinction between Models 1 and 2 lies in the thickness of the shell elements representing the concrete members, defined as 0.25 m and 0.40 m, respectively. The placement of the steel rings along the tunnel axis is shown in Fig. 6 . The numerical simulation of the TBM tunneling process was performed using a staged construction approach within PLAXIS 3D, designed to replicate the complex sequential steps of tunnel excavation and lining installation. In the initial phase of the analysis, the in-situ stresses within the ground model were generated using the K0​ procedure, establishing the pre-excavation stress state based on the defined soil properties. Following the initial stress generation, the simulation proceeded through a series of sequential excavation and lining installation steps. It was assumed that the first 25 meters of the tunnel had already been excavated and lined. Subsequent stages of excavation were then modelled incrementally, with each phase representing the advancement of the tunnel by one segment length (1.5 m or 0.25 m). During the excavation stages, three primary load conditions were applied uniformly: TBM Face Pressure: A uniform pressure of -750 kN/m 2 was applied, acting normal to the excavation face to represent active ground resistance. Tail Void Grouting Pressure: A uniform pressure of -500 kN/m 2 was applied immediately behind the shield to model the stabilization of the annular void. TBM Jacking Force: A constant thrust pressure of 3500 kN/m 2 was applied normal to the cross-section of the segmental lining at the tunnel tail, simulating the machine's advancement force. Crucially, the staged analysis was carried out over a total of 18 distinct phases for all three models (Model 1, Model 2, and Model 3). This uniform phase count was established because the steel rings (in Model 3) and their 0.25 m wide reinforced concrete equivalents (in Model 1 and Model 2) were strategically placed every third segment ring. Specifically, 5 of these 18 phases were dedicated to the installation and activation of these special ring/equivalent elements, ensuring a direct and consistent comparison of the structural behaviour across all three design configurations. All comparisons of deformation, force, and moment values among the different tunnel models were specifically made based on the results obtained after the final staged construction phase, representing the full simulated tunnel length and long-term equilibrium conditions. To quantitatively assess and compare the structural benefits of each tunnel model, a suite of key performance indicators (KPIs) was meticulously extracted from the PLAXIS 3D simulations. While displacement values, by the nature of TBM tunneling, may not always present a dramatically visible difference, the primary focus of this analysis was placed on the internal forces and moments within the lining elements, as these are critical indicators of structural integrity and potential failure. The selected KPIs included: Deformations : Total displacements at segmental lining (∣u∣ or u total ​). Axial Forces : Axial forces in the longitudinal direction (N 1 ​) and axial forces in the cross-sectional direction (N 2 ​). Shear Forces : Shear forces in the 1–2 (local axis) plane (Q 12 ​), shear forces in the 2–3 (local axis) plane (Q 23 ​), and shear forces in the 1–3 (local axis) plane (Q 13 ​). Bending Moments : Bending moments in the 1–1 direction (M 11 ​) and bending moments in the 2–2 direction (M 22 ​). Torsion Moments : Torsion moments in the 1–2 direction (M 12 ​). Moment-Interaction Diagrams for Reinforced Concrete Segments : The diagrams are showing the capacity of the reinforced concrete segments with the corresponding axial forces (N 2 ) and moments (M 11 ). 3. Results The findings are presented in terms of ground and lining deformations, and the distribution of axial forces, shear forces, bending/torsion moments within the lining elements, and moment interaction diagrams of the segmental linings. The data are extracted from the numerical models, specifically focusing on critical points and overall distributions to provide a comprehensive comparison. Total Deformations The simulation results indicate distinct deformation patterns for each tunnel model. Figure 7 illustrates the total deformation at the lining system in a bar chart. For every point of the models, the deformations of the Model 3 are equal or smaller than the Model 2. Axial Forces in Cross-Sectional Directions (N 2 ) Given that the primary load-carrying mechanism and the most critical stresses in the segmental rings are predominantly observed in the cross-sectional plane, the N 2 (the axial force cross-sectional direction) were selected as the most appropriate metric for direct comparison between the models. To provide a comprehensive assessment of the load-carrying performance of the segments and the steel rings, the maximum values of the N 2 axial forces were extracted and compared across the three distinct design configurations (see Fig. 8 ). Shear Forces For the purpose of a direct and relevant structural comparison within the segmental lining, the shear force in the 1–2 direction (Q12) was deemed the most appropriate indicator. This selection is based on its direct relevance to the primary load transfer across the segment interfaces and the composite action between the concrete and the steel rings. Accordingly, the maximum shear forces in the Q12 direction are presented and visually compared in Fig. 9 , highlighting the performance differences across the three tunnel models. Bending Moments For the assessment of structural performance and the efficacy of the steel ring reinforcement, the M 11 bending moments were established as the key comparative criterion. This selection is based on the critical observation that the M 11 moment represents the bending demand that attempts to bend the tunnel cross-section inward, similar to how a column is subjected to bending. Since the lining's most critical load-bearing mechanism and potential failure mode are often associated with this transverse flexural behaviour, the M 11 moments are considered the most defining moment values. Accordingly, the maximum M 11 moment values are systematically compared in the subsequent analysis figures to quantify the structural benefits across the three model configurations (see Fig. 10 ). Member Forces in Steel Rings To confirm the structural viability of the proposed steel ring, a simple interaction check for combined axial load and bending moment was performed based on the maximum forces derived from the PLAXIS 3D model. The steel ring, defined with a 0.25 m x 0.25 m solid rectangular cross-section and S355 steel, was subjected to the maximum calculated axial load (N = 13000 kN) and bending moment (M = 87 kNm). The resulting interaction ratio, 0.658 confirms that the steel ring possesses sufficient structural capacity to sustain the transferred ground loads. This result validates the robustness of the integrated reinforcement, demonstrating that it can effectively support internal forces with a reliable safety margin and serves as a feasible supplementary element for optimized TBM linings. Segmental Lining Interaction Curves The interaction curves were generated based on the relationship between the transverse axial force (N 2 ) and the longitudinal bending moment (M 11 ) acting on the segments. The ultimate capacity of the reinforced concrete sections was defined using the following details: Section Width (b): 1500 mm Section Depths (h): 250 mm or 400 mm Reinforcement Details: Each segment cross-section included two layers of Φ8 mm diameter reinforcement bars, placed at 100 mm center-to-center spacing. The N 2 and M 11 force-moment pairs, extracted from every node point in the PLAXIS 3D analysis, were plotted directly onto the segment's theoretical N-M capacity curve to assess the structural demand relative to the ultimate capacity. The analysis focuses on the most critical zone, specifically the region located between the first and second steel ring rows, where the axial forces reach their peak. The resulting interaction curves and their corresponding analysis data points are presented in Fig. 11 (40 cm without steel ring) and Fig. 12 (25 cm with steel ring). The values of the moments are taken as absolute values, because of the symmetrical nature of the capacity diagram along the axial force axis. 4. Discussion 4.1. Deformational Behaviour and Structural Stability The deformational analysis indicates that the integration of steel rings leads to a slight reduction in overall displacements compared to the lining without steel rings. While the steel-ring-reinforced model exhibits lower deformations, the difference in displacement magnitude between the two configurations remains limited. Similar trends have been reported in previous numerical studies, where stiffness-enhancing measures primarily contributed to improved deformation control rather than substantial reductions in global convergence [ 8 ], [ 12 ], [ 17 ]. The presence of supplementary support elements contributes positively to the structural stability of TBM tunnel linings by increasing confinement and overall system stiffness [ 13 ], [ 18 ], [ 32 ]. In particular, steel rings can act as a stabilizing structural component that limits localized deformations and improves the lining’s resilience against unfavourable ground conditions or construction-related irregularities. This effect is especially relevant when reduced segment thickness is adopted for material and cost optimization, as thinner linings are generally more sensitive to stress concentrations and joint behaviour [ 29 ]. 4.2. Internal Forces and Stress Redistribution The numerical results reveal distinct patterns of load redistribution associated with the presence of steel rings. The maximum shear force (Q) values at the segments show only marginal differences between the model with and without steel rings, which can be attributed to the dominant role of segmental joints in governing shear transfer in TBM linings. However, localized force concentrations around the steel rings reduce shear demand within the concrete segment body, indicating a more favourable stress state for the concrete [ 20 ], [ 32 ], [ 36 ]. Regarding axial forces, the longitudinal component (N 1 ) reflects the contribution of steel rings along the tunnel axis, while the circumferential axial force (N 2 ) provides clearer evidence of their structural efficiency [ 18 ], [ 41 ]. Since N 2 forces are primarily responsible for resisting overburden loads and maintaining ring stability, the ability of steel rings to absorb a significant portion of these forces is structurally advantageous. A similar behavior is observed for bending moments. Among the evaluated components, the transverse bending moment M 11 shows the most pronounced reduction in the concrete segments due to the presence of steel rings. This indicates that the steel rings effectively attract a higher share of bending demand, allowing the thinner concrete segments to safely resist the remaining loads. The N–M interaction analysis further supports these findings. All N 2 –M 11 load combinations obtained from the numerical model fall within the safe capacity domain of the interaction diagrams for the adopted cross-sections, confirming the structural adequacy of both the conventional and optimized lining configurations. 4.3. Implications for Design Optimization and Sustainability The results indicate that the use of internal steel rings enables a performance-based optimization of TBM tunnel linings. The analyses demonstrate that 25 cm thick segments reinforced with steel rings can achieve structural performance comparable to that of conventional 40 cm thick unreinforced segments. Similar optimization approaches have been discussed in the literature as effective strategies for improving structural efficiency without compromising safety [ 13 ], [ 17 ], [ 29 ]. The reduction in segment thickness results in a concrete volume saving of approximately 5.2 m³ per linear meter of tunnel, corresponding to a 43.7% decrease in concrete consumption. In addition to material savings, the reduced lining thickness allows for a smaller excavation diameter, leading to lower excavation volumes and improved construction logistics [ 2 ], [ 13 ], [ 29 ], [ 46 ]. Although the inclusion of steel rings introduces an additional steel demand of 2.83 tonnes per meter, the overall balance remains favourable due to the substantial reduction in concrete usage. Beyond construction efficiency, the improved deformation control and reduced bending moments observed in the reinforced lining contribute to enhanced structural robustness and may support a longer service life with reduced maintenance requirements [ 15 ], [ 22 ], [ 47 ]. Furthermore, the significant reduction in concrete consumption aligns with sustainability objectives by lowering the embodied carbon footprint of the tunnel lining system [ 28 ], [ 29 ], [ 46 ]. 5. Conclusions This study successfully executed a comprehensive numerical comparative analysis utilizing the PLAXIS 3D Finite Element Method to rigorously investigate the structural efficacy of integrating internal steel rings as a novel strategy for optimizing TBM segmental linings. The investigation provided quantitative evidence that the 25 cm thin segments, when reinforced with strategically placed steel rings, achieve structural performance levels comparable to, or even superior to, conventional 40 cm thick unsupported segments under challenging rock mass and high overburden conditions. The primary structural benefit stems from the superior load redistribution mechanism: the steel rings effectively manage and absorb substantial N 2 axial forces, consequently reducing the critical M 11 bending moments and flexural demands on the concrete elements. This enhancement in load transfer is robustly validated by the N-M interaction analysis, which confirmed that the loading points for the thin, reinforced segments fall well within the ultimate capacity curve, thereby maintaining a significant structural safety margin. The design innovation yields tangible economic and environmental advantages, translating directly into an approximate 43.7% reduction in concrete volume per linear meter of the tunnel, which not only lowers material costs but also reduces the necessary excavation diameter and streamlines logistics. In conclusion, the strategic use of steel rings represents a validated, performance-based approach for achieving material optimization in TBM tunnel design without compromising safety, paving the way for more economical and sustainable underground infrastructure projects. While this study provides valuable insights, it is important to acknowledge certain limitations and identify areas for future research. The results are limited to the chosen soil type and valid for a certain behaviour for segment joints and specific steel ring configuration. Moreover, the current analysis is static and dynamic loads (e.g., seismic), long-term creep, shrinkage, and ground-structure interaction over extended periods are not considered. Future work should focus on the parametric optimization of ring design (spacing and cross-sectional geometry), investigation of long-term and dynamic load effects, and full-scale experimental validation to further enhance the practical applicability of this innovative system. Also, a detailed economic analysis, integrating the costs of materials, installation, and long-term maintenance, would be beneficial to fully quantify the economic advantages of steel ring integration. Declarations Competing Interests The authors declare no competing interests. Funding This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. Author Contribution C.Ç.: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data Curation, Writing - Original Draft, Writing - Review & Editing, Visualization.B.U.: Conceptualization, Methodology, Resources, Writing - Review & Editing, Supervision, Project administration.C.G.: Conceptualization, Validation, Investigation, Writing - Review & Editing. All authors have read and agreed to the published version of the manuscript. Data Availability The datasets generated and analyzed during the current study (specifically the PLAXIS 3D numerical models and extracted structural force data) are available from the corresponding author on reasonable request. References Gong, Q., Yin, L., Ma, H. & Zhao, J. TBM tunnelling under adverse geological conditions: An overview. Tunn. Undergr. Space Technol. 57 , 4–17. 10.1016/j.tust.2016.04.002 (Mar. 2016). Bilgin, N. & Acun, S. Practical Management of Tunneling with Tunnel Boring Machines . 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19:52:19","extension":"html","order_by":28,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":131221,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8554968/v1/21ecb736e5e9ec135df1b715.html"},{"id":100449550,"identity":"7f340106-35c9-467f-8007-3bac11b2f5c9","added_by":"auto","created_at":"2026-01-16 19:52:18","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":13414,"visible":true,"origin":"","legend":"\u003cp\u003eVertical cross section of the tunnel model\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8554968/v1/caa9872808ddec14b151a719.png"},{"id":100546847,"identity":"65193a77-167f-4ce3-98fc-42f562a9bac8","added_by":"auto","created_at":"2026-01-19 08:12:56","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":61168,"visible":true,"origin":"","legend":"\u003cp\u003eReinforcement placement of the concrete segments\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8554968/v1/8d68a78f9290b8d1804a01a4.png"},{"id":100546955,"identity":"e6d6bf83-d036-43a9-a44a-50aa08fe270d","added_by":"auto","created_at":"2026-01-19 08:13:32","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":31360,"visible":true,"origin":"","legend":"\u003cp\u003eSteel ring cross section and complete steel ring structure\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8554968/v1/cfaa9f0dfe9d9b1197c59fab.png"},{"id":100449554,"identity":"828cc8f5-f381-4ec9-816b-f7a67cbf9745","added_by":"auto","created_at":"2026-01-16 19:52:18","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":103904,"visible":true,"origin":"","legend":"\u003cp\u003e3D view of the PLAXIS 3D model\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8554968/v1/c918a34ca869378db93c205c.png"},{"id":100449553,"identity":"f0acc800-8c67-4638-9e12-d89f8ff7edbe","added_by":"auto","created_at":"2026-01-16 19:52:18","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":41140,"visible":true,"origin":"","legend":"\u003cp\u003eProfile view of the PLAXIS 3D model\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8554968/v1/26760654ac1c29cce48af68b.png"},{"id":100547263,"identity":"ccc70c9b-a4a1-46f8-afa6-fd93a6eaedff","added_by":"auto","created_at":"2026-01-19 08:15:03","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":21862,"visible":true,"origin":"","legend":"\u003cp\u003eSteel ring placement along the tunnel axis\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8554968/v1/444fd4589e9a16877cc1aef8.png"},{"id":100547688,"identity":"3b4c4ead-b356-4a89-ad9b-ffbdc936c63a","added_by":"auto","created_at":"2026-01-19 08:16:19","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":76154,"visible":true,"origin":"","legend":"\u003cp\u003eMaximum total deformation at lining system\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-8554968/v1/a2926b74a9e757e98aea6886.png"},{"id":100547860,"identity":"046d7610-8f3c-46f0-a650-e31ce936746c","added_by":"auto","created_at":"2026-01-19 08:16:47","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":50756,"visible":true,"origin":"","legend":"\u003cp\u003eMaximum axial forces (N\u003csub\u003e2\u003c/sub\u003e) at lining system\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-8554968/v1/f902c0dd5eccecadf440ea2b.png"},{"id":100449570,"identity":"b5976b03-b0d2-43ee-bc18-ce67b2d5f807","added_by":"auto","created_at":"2026-01-16 19:52:19","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":54136,"visible":true,"origin":"","legend":"\u003cp\u003eMaximum shear forces (Q\u003csub\u003e12\u003c/sub\u003e) at lining system\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-8554968/v1/a2dbb8be1965d28e8c54155e.png"},{"id":100449566,"identity":"e9035658-9f09-4d08-bbe7-2ce2cae37d12","added_by":"auto","created_at":"2026-01-16 19:52:19","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":48203,"visible":true,"origin":"","legend":"\u003cp\u003eMinimum bending moments (M\u003csub\u003e11\u003c/sub\u003e) at lining system\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-8554968/v1/ea1aaf927fc5a91ce6ea0a75.png"},{"id":100548086,"identity":"b6b242f0-c1dd-43fa-b2fa-cea719c25b78","added_by":"auto","created_at":"2026-01-19 08:17:29","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":75002,"visible":true,"origin":"","legend":"\u003cp\u003eN-M curve of segmental lining between first and second ring row of Model 2\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-8554968/v1/995194364fc864564678d173.png"},{"id":100449564,"identity":"4ded9713-ebdd-4e4e-94a3-248ce774ddc2","added_by":"auto","created_at":"2026-01-16 19:52:18","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":84413,"visible":true,"origin":"","legend":"\u003cp\u003eN-M curve of segmental lining between first and second ring row of Model 3\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-8554968/v1/f60feee16b51e558c0a85ff1.png"},{"id":109524808,"identity":"9b35e0fa-c31f-42ab-89bf-6faac959fafd","added_by":"auto","created_at":"2026-05-19 06:56:50","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":829120,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8554968/v1/98abc34e-1477-4291-b589-1b66d652c18d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Novel Approach for the Optimization of Segmental Linings in TBM Tunnels through Steel Ring Reinforcement","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe rising demands of global urbanization and the ongoing necessity for strong infrastructure have established Mechanized Tunnelling, mainly using Tunnel Boring Machines (TBMs), as the most effective approach for constructing underground facilities in heavily populated urban areas and challenging geological conditions [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. The effective implementation and sustained performance of these projects are primarily reliant on the structural effectiveness of precast concrete segmental linings [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. These linings act as the main structural support, withstanding intricate geotechnical loads and ensuring tunnel stability. Precast concrete segments are widely employed because of their quick installation, excellent compressive strength, and modular design, enabling accurate and controlled assembly as the tunnel progresses [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. These components are required to resist a complex set of loads, such as radial ground pressures, bending moments, and axial forces that are transferred through the interconnected tunnel ring system [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eDespite their many benefits, TBM segmental linings also present certain structural challenges. A major issue is the formation of high stress concentrations, commonly occurring at the joints between segments, which act as critical zones of structural vulnerability [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Moreover, in difficult geological conditions\u0026mdash;such as squeezing ground, highly deformable soft clays, or zones with considerable ground relaxation\u0026mdash;segmental linings may undergo excessive deformation, which can adversely affect their long-term stability and structural integrity [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. This challenge is further intensified by uncertainties associated with insufficient in-situ geotechnical information. Such gaps can result in overly conservative designs\u0026mdash;leading to unnecessary material use and higher costs\u0026mdash;or, more critically, under-designed systems that introduce significant structural and safety risks [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. To reduce material usage and construction costs while improving structural performance, various alternative approaches have been investigated, such as employing high-performance concrete or implementing prestressed lining systems [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e], [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Although successful in certain applications, these approaches often add construction complexity or rely on costly specialized materials, which can diminish the expected benefits. Consequently, finding a practical and efficient way to enhance the mechanical performance of thinner segments continues to be an important research challenge [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTBM linings resist ground pressures through axial compression and flexural resistance [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e], [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e], though segment joints often create stress concentrations that risk structural damage [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e], [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eWhile reducing segment thickness offers economic and environmental benefits by decreasing volume of excavation, it significantly lowers lining stiffness and increases vulnerability to deformation [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e], [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. Inspired by the efficacy of steel arches in NATM [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e], [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e], [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e], this study explores internal steel rings to maintain stability in thinner TBM segments.\u003c/p\u003e \u003cp\u003eDespite the prevalence of numerical modeling in tunnel engineering [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e], [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e], [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e], [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e], a research gap exists in quantifying the specific impact of steel rings on TBM lining performance.\u003c/p\u003e \u003cp\u003eThis study is therefore specifically designed to bridge this identified critical research gap. By performing a rigorous numerical comparative analysis using PLAXIS 3D, we evaluated the structural performance across three distinct model configurations: (1) 25 cm thin segments without reinforcement, (2) reference 40 cm thick segments without reinforcement, and (3) 25 cm thin segments strategically reinforced with steel rings. The analysis focuses on key performance indicators, including total displacement, the distribution patterns of axial (N2) and shear forces (Q12), and critical bending moments (M11), with the goal of definitively ascertaining whether this integrated system can reliably achieve superior structural performance while allowing for substantial material optimization. This approach aligns with the broader objective of achieving performance-based optimization for future TBM-driven tunneling projects.\u003c/p\u003e"},{"header":"2. Methodology","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Numerical Modelling Software and Approach\u003c/h2\u003e \u003cp\u003eFor the numerical modelling in this study, the PLAXIS 3D software was utilized (Potts \u0026amp; Zdravkovid, 1999; Sakil Ahmed et al., 2023). The dimensions of the numerical models were carefully determined to be sufficiently large, thereby encompassing the full influence zone of the tunnel excavation within the surrounding ground. Consequently, for all three distinct tunnel models investigated, the overall dimensions were consistently set at 25 m (width) x 85 m (depth) x 100 m (length). The tunnel excavation process was specifically modelled to advance along the Y-axis of the coordinate system. Due to the inherent symmetrical nature of the tunnel structure, which implies symmetrical distributions of resulting deformations and stresses, modelling only the left half of the tunnel was sufficient for obtaining accurate and representative results.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Ground Conditions and Material Properties\u003c/h2\u003e \u003cp\u003eAn idealized, homogeneous ground profile was defined for the analysis. To create a representative and challenging scenario for the tunnel-ground interaction, the profile was simplified to a single, deep layer of Claystone.\u003c/p\u003e \u003cp\u003eThe tunnel axis was placed at an elevation of -11.25 m, which resulted in a significant overburden depth of 71.25 m from the ground surface (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The groundwater table was positioned at the 0.00 m to ensure saturated conditions around the tunnel and to contribute to the high-stress environment. The Hoek-Brown material model was chosen to accurately simulate the non-linear behaviour of the rock mass under stress. The specific parameters for the Claystone are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRock mass parameters of Claystone employed in the study\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnit\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElevation Range\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e+\u0026thinsp;60.0 m to -25.0 m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eUniaxial Compressive Strength (intact rock), σci​\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMPa\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGeological Strength Index (GSI)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaterial Constant (intact rock), mi​\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDisturbance Factor, D\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eUnit Weight, γ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ekN/m\u0026sup3;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRock Mass Deformation Modulus, Erm​\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGPa\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePoisson's Ratio, ν\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo allow for a more robust comparison of axial loads, shear forces, and moments within the reinforced concrete lining material in the analyses, parameters reflecting linear elastic material behaviour suitable for shell elements were adopted. The specific properties for the concrete lining, which were defined for plate elements in PLAXIS 3D, are detailed in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Representing lining elements as continuum soil elements was avoided in PLAXIS 3D to facilitate the direct extraction and comparison of internal structural forces (axial loads, shear forces, and bending moments) from such units. Reinforcement placement of the concrete segments is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e for both 25 cm and 40 cm thick segments.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eLinear Elastic Parameters for Concrete Segmental Linings\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnit\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThickness (d)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.25 or 0.40 (variable)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003em\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eUnit Weight, γ\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ekN/m\u0026sup3;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMaterial Model\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLinear Elastic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eIsotropic\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eYoung's Modulus, E\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGPa\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePoisson's Ratio, ν\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe steel ring elements, which constitute a central focus of this study, were defined as a linear elastic material model and represented as shell elements. For Model 3 (25 cm segments with rings), the thickness of these elements was set at 0.25 m. The specific material properties used for the steel rings are detailed in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. A perfect bond was assumed between the steel rings and the concrete segments in the numerical model, implying full composite action and ensuring the structural integrity of the tunnel body. These steel elements, similar to reinforced concrete segments, were modelled to be assembled in sections within the tunnel to form a circular shape conforming to the tunnel geometry. The cross section of the steel ring and complete ring structure from tunnel cross section are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eLinear Elastic Parameters for Steel Rings\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnit\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThickness (d)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003em\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eUnit Weight, γ\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e78.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ekN/m\u0026sup3;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMaterial Model\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLinear Elastic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eIsotropic\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eYoung's Modulus, E\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGPa\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePoisson's Ratio, ν\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA simplified representation of the TBM shield body was incorporated into the numerical model. This TBM body was defined using plate elements with linear elastic material properties, designed to symbolize the presence and effect of the advancing machine within the excavation. The specific parameters utilized for the TBM shield are presented in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Notably, the unit weight of 247 kN/m\u0026sup3; was adopted for the TBM shield, consistent with recommendations found in the PLAXIS 3D manual [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eLinear Elastic Parameters for the TBM Shield Body\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnit\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eThickness (d)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003em\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eUnit Weight, γ\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e247\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ekN/m\u0026sup3;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMaterial Model\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLinear Elastic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eIsotropic\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eYoung's Modulus, E\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGPa\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePoisson's Ratio, ν\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe 3D and profile views of the model are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Geometric Model and Discretization\u003c/h2\u003e \u003cp\u003eThe internal diameter of the tunnel was set at 8 meters for each individual model configuration. For sections with a segment thickness of 25 cm, the external tunnel diameter was 8.50 m, while for section with a segment thickness of 40 cm, the external tunnel diameter was 8.80 m. The total length of the modelled tunnel section was defined to minimize boundary effects. The depth of the tunnel axis from the ground surface was 71.25 m.\u003c/p\u003e \u003cp\u003eThe tunnel lining segments were modelled as rectangular-section segments, curving to conform to the tunnel's circular geometry. Each segment possessed a constant width of 1.5 m in the longitudinal direction of the tunnel axis, corresponding to a single excavation step of 1.5 m during the tunnel advancement simulation. The segment thicknesses varied according to the specific model configuration:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eModel 1: 25 cm thick concrete segments without steel rings.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eModel 2: 40 cm thick concrete segments without steel rings.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eModel 3: 25 cm thick concrete segments with strategically placed steel rings.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThe internal steel rings were designed with a solid rectangular cross-section. Initial trials considered a ring width of 0.20 m; however, based on preliminary assessments of efficiency, a width of 0.25 m was ultimately adopted for these rings, which were positioned along the tunnel axis. Regarding longitudinal placement, while an initial consideration involved installing steel rings every five concrete segments, leading to a 7.5 m spacing, this interval was deemed too large. Consequently, a more accurate and effective placement strategy was chosen, involving the installation of steel rings every three concrete segments along the tunnel's longitudinal direction, resulting in a consistent spacing of 4.5 m (3 segments x 1.5 m/segment). These steel rings were also represented using shell elements in the numerical model. For the models 1 and 2, the steel rings are geometrically placed as in the model 3. The primary distinction between Models 1 and 2 lies in the thickness of the shell elements representing the concrete members, defined as 0.25 m and 0.40 m, respectively. The placement of the steel rings along the tunnel axis is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe numerical simulation of the TBM tunneling process was performed using a staged construction approach within PLAXIS 3D, designed to replicate the complex sequential steps of tunnel excavation and lining installation.\u003c/p\u003e \u003cp\u003eIn the initial phase of the analysis, the in-situ stresses within the ground model were generated using the K0​ procedure, establishing the pre-excavation stress state based on the defined soil properties.\u003c/p\u003e \u003cp\u003eFollowing the initial stress generation, the simulation proceeded through a series of sequential excavation and lining installation steps. It was assumed that the first 25 meters of the tunnel had already been excavated and lined. Subsequent stages of excavation were then modelled incrementally, with each phase representing the advancement of the tunnel by one segment length (1.5 m or 0.25 m).\u003c/p\u003e \u003cp\u003eDuring the excavation stages, three primary load conditions were applied uniformly:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eTBM Face Pressure: A uniform pressure of -750 kN/m\u003csup\u003e2\u003c/sup\u003e was applied, acting normal to the excavation face to represent active ground resistance.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eTail Void Grouting Pressure: A uniform pressure of -500 kN/m\u003csup\u003e2\u003c/sup\u003e was applied immediately behind the shield to model the stabilization of the annular void.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eTBM Jacking Force: A constant thrust pressure of 3500 kN/m\u003csup\u003e2\u003c/sup\u003e was applied normal to the cross-section of the segmental lining at the tunnel tail, simulating the machine's advancement force.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eCrucially, the staged analysis was carried out over a total of 18 distinct phases for all three models (Model 1, Model 2, and Model 3). This uniform phase count was established because the steel rings (in Model 3) and their 0.25 m wide reinforced concrete equivalents (in Model 1 and Model 2) were strategically placed every third segment ring. Specifically, 5 of these 18 phases were dedicated to the installation and activation of these special ring/equivalent elements, ensuring a direct and consistent comparison of the structural behaviour across all three design configurations.\u003c/p\u003e \u003cp\u003eAll comparisons of deformation, force, and moment values among the different tunnel models were specifically made based on the results obtained after the final staged construction phase, representing the full simulated tunnel length and long-term equilibrium conditions.\u003c/p\u003e \u003cp\u003eTo quantitatively assess and compare the structural benefits of each tunnel model, a suite of key performance indicators (KPIs) was meticulously extracted from the PLAXIS 3D simulations. While displacement values, by the nature of TBM tunneling, may not always present a dramatically visible difference, the primary focus of this analysis was placed on the internal forces and moments within the lining elements, as these are critical indicators of structural integrity and potential failure. The selected KPIs included:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eDeformations\u003c/b\u003e: Total displacements at segmental lining (∣u∣ or u\u003csub\u003etotal\u003c/sub\u003e​).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eAxial Forces\u003c/b\u003e: Axial forces in the longitudinal direction (N\u003csub\u003e1\u003c/sub\u003e​) and axial forces in the cross-sectional direction (N\u003csub\u003e2\u003c/sub\u003e​).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eShear Forces\u003c/b\u003e: Shear forces in the 1\u0026ndash;2 (local axis) plane (Q\u003csub\u003e12\u003c/sub\u003e​), shear forces in the 2\u0026ndash;3 (local axis) plane (Q\u003csub\u003e23\u003c/sub\u003e​), and shear forces in the 1\u0026ndash;3 (local axis) plane (Q\u003csub\u003e13\u003c/sub\u003e​).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eBending Moments\u003c/b\u003e: Bending moments in the 1\u0026ndash;1 direction (M\u003csub\u003e11\u003c/sub\u003e​) and bending moments in the 2\u0026ndash;2 direction (M\u003csub\u003e22\u003c/sub\u003e​).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eTorsion Moments\u003c/b\u003e: Torsion moments in the 1\u0026ndash;2 direction (M\u003csub\u003e12\u003c/sub\u003e​).\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eMoment-Interaction Diagrams for Reinforced Concrete Segments\u003c/b\u003e: The diagrams are showing the capacity of the reinforced concrete segments with the corresponding axial forces (N\u003csub\u003e2\u003c/sub\u003e) and moments (M\u003csub\u003e11\u003c/sub\u003e).\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cp\u003eThe findings are presented in terms of ground and lining deformations, and the distribution of axial forces, shear forces, bending/torsion moments within the lining elements, and moment interaction diagrams of the segmental linings. The data are extracted from the numerical models, specifically focusing on critical points and overall distributions to provide a comprehensive comparison.\u003c/p\u003e \u003cp\u003e \u003cb\u003eTotal Deformations\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe simulation results indicate distinct deformation patterns for each tunnel model. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e illustrates the total deformation at the lining system in a bar chart. For every point of the models, the deformations of the Model 3 are equal or smaller than the Model 2.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eAxial Forces in Cross-Sectional Directions (N\u003c/b\u003e \u003csub\u003e \u003cb\u003e2\u003c/b\u003e \u003c/sub\u003e \u003cb\u003e)\u003c/b\u003e \u003c/p\u003e \u003cp\u003eGiven that the primary load-carrying mechanism and the most critical stresses in the segmental rings are predominantly observed in the cross-sectional plane, the N\u003csub\u003e2\u003c/sub\u003e (the axial force cross-sectional direction) were selected as the most appropriate metric for direct comparison between the models. To provide a comprehensive assessment of the load-carrying performance of the segments and the steel rings, the maximum values of the N\u003csub\u003e2\u003c/sub\u003e axial forces were extracted and compared across the three distinct design configurations (see Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eShear Forces\u003c/b\u003e \u003c/p\u003e \u003cp\u003eFor the purpose of a direct and relevant structural comparison within the segmental lining, the shear force in the 1\u0026ndash;2 direction (Q12) was deemed the most appropriate indicator. This selection is based on its direct relevance to the primary load transfer across the segment interfaces and the composite action between the concrete and the steel rings. Accordingly, the maximum shear forces in the Q12 direction are presented and visually compared in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, highlighting the performance differences across the three tunnel models.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eBending Moments\u003c/b\u003e \u003c/p\u003e \u003cp\u003eFor the assessment of structural performance and the efficacy of the steel ring reinforcement, the M\u003csub\u003e11\u003c/sub\u003e bending moments were established as the key comparative criterion. This selection is based on the critical observation that the M\u003csub\u003e11\u003c/sub\u003e moment represents the bending demand that attempts to bend the tunnel cross-section inward, similar to how a column is subjected to bending. Since the lining's most critical load-bearing mechanism and potential failure mode are often associated with this transverse flexural behaviour, the M\u003csub\u003e11\u003c/sub\u003e moments are considered the most defining moment values. Accordingly, the maximum M\u003csub\u003e11\u003c/sub\u003e moment values are systematically compared in the subsequent analysis figures to quantify the structural benefits across the three model configurations (see Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eMember Forces in Steel Rings\u003c/b\u003e \u003c/p\u003e \u003cp\u003eTo confirm the structural viability of the proposed steel ring, a simple interaction check for combined axial load and bending moment was performed based on the maximum forces derived from the PLAXIS 3D model. The steel ring, defined with a 0.25 m x 0.25 m solid rectangular cross-section and S355 steel, was subjected to the maximum calculated axial load (N\u0026thinsp;=\u0026thinsp;13000 kN) and bending moment (M\u0026thinsp;=\u0026thinsp;87 kNm). The resulting interaction ratio, 0.658 confirms that the steel ring possesses sufficient structural capacity to sustain the transferred ground loads. This result validates the robustness of the integrated reinforcement, demonstrating that it can effectively support internal forces with a reliable safety margin and serves as a feasible supplementary element for optimized TBM linings.\u003c/p\u003e \u003cp\u003e \u003cb\u003eSegmental Lining Interaction Curves\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe interaction curves were generated based on the relationship between the transverse axial force (N\u003csub\u003e2\u003c/sub\u003e) and the longitudinal bending moment (M\u003csub\u003e11\u003c/sub\u003e) acting on the segments. The ultimate capacity of the reinforced concrete sections was defined using the following details:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eSection Width (b): 1500 mm\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eSection Depths (h): 250 mm or 400 mm\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eReinforcement Details: Each segment cross-section included two layers of Φ8 mm diameter reinforcement bars, placed at 100 mm center-to-center spacing.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThe N\u003csub\u003e2\u003c/sub\u003e and M\u003csub\u003e11\u003c/sub\u003e force-moment pairs, extracted from every node point in the PLAXIS 3D analysis, were plotted directly onto the segment's theoretical N-M capacity curve to assess the structural demand relative to the ultimate capacity. The analysis focuses on the most critical zone, specifically the region located between the first and second steel ring rows, where the axial forces reach their peak. The resulting interaction curves and their corresponding analysis data points are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e (40 cm without steel ring) and Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e (25 cm with steel ring). The values of the moments are taken as absolute values, because of the symmetrical nature of the capacity diagram along the axial force axis.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4. Discussion","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Deformational Behaviour and Structural Stability\u003c/h2\u003e \u003cp\u003eThe deformational analysis indicates that the integration of steel rings leads to a slight reduction in overall displacements compared to the lining without steel rings. While the steel-ring-reinforced model exhibits lower deformations, the difference in displacement magnitude between the two configurations remains limited. Similar trends have been reported in previous numerical studies, where stiffness-enhancing measures primarily contributed to improved deformation control rather than substantial reductions in global convergence [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe presence of supplementary support elements contributes positively to the structural stability of TBM tunnel linings by increasing confinement and overall system stiffness [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. In particular, steel rings can act as a stabilizing structural component that limits localized deformations and improves the lining\u0026rsquo;s resilience against unfavourable ground conditions or construction-related irregularities. This effect is especially relevant when reduced segment thickness is adopted for material and cost optimization, as thinner linings are generally more sensitive to stress concentrations and joint behaviour [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Internal Forces and Stress Redistribution\u003c/h2\u003e \u003cp\u003eThe numerical results reveal distinct patterns of load redistribution associated with the presence of steel rings. The maximum shear force (Q) values at the segments show only marginal differences between the model with and without steel rings, which can be attributed to the dominant role of segmental joints in governing shear transfer in TBM linings. However, localized force concentrations around the steel rings reduce shear demand within the concrete segment body, indicating a more favourable stress state for the concrete [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eRegarding axial forces, the longitudinal component (N\u003csub\u003e1\u003c/sub\u003e) reflects the contribution of steel rings along the tunnel axis, while the circumferential axial force (N\u003csub\u003e2\u003c/sub\u003e) provides clearer evidence of their structural efficiency [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. Since N\u003csub\u003e2\u003c/sub\u003e forces are primarily responsible for resisting overburden loads and maintaining ring stability, the ability of steel rings to absorb a significant portion of these forces is structurally advantageous.\u003c/p\u003e \u003cp\u003eA similar behavior is observed for bending moments. Among the evaluated components, the transverse bending moment M\u003csub\u003e11\u003c/sub\u003e shows the most pronounced reduction in the concrete segments due to the presence of steel rings. This indicates that the steel rings effectively attract a higher share of bending demand, allowing the thinner concrete segments to safely resist the remaining loads.\u003c/p\u003e \u003cp\u003eThe N\u0026ndash;M interaction analysis further supports these findings. All N\u003csub\u003e2\u003c/sub\u003e\u0026ndash;M\u003csub\u003e11\u003c/sub\u003e load combinations obtained from the numerical model fall within the safe capacity domain of the interaction diagrams for the adopted cross-sections, confirming the structural adequacy of both the conventional and optimized lining configurations.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e4.3. Implications for Design Optimization and Sustainability\u003c/h2\u003e \u003cp\u003eThe results indicate that the use of internal steel rings enables a performance-based optimization of TBM tunnel linings. The analyses demonstrate that 25 cm thick segments reinforced with steel rings can achieve structural performance comparable to that of conventional 40 cm thick unreinforced segments. Similar optimization approaches have been discussed in the literature as effective strategies for improving structural efficiency without compromising safety [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe reduction in segment thickness results in a concrete volume saving of approximately 5.2 m\u0026sup3; per linear meter of tunnel, corresponding to a 43.7% decrease in concrete consumption. In addition to material savings, the reduced lining thickness allows for a smaller excavation diameter, leading to lower excavation volumes and improved construction logistics [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. Although the inclusion of steel rings introduces an additional steel demand of 2.83 tonnes per meter, the overall balance remains favourable due to the substantial reduction in concrete usage.\u003c/p\u003e \u003cp\u003eBeyond construction efficiency, the improved deformation control and reduced bending moments observed in the reinforced lining contribute to enhanced structural robustness and may support a longer service life with reduced maintenance requirements [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]. Furthermore, the significant reduction in concrete consumption aligns with sustainability objectives by lowering the embodied carbon footprint of the tunnel lining system [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eThis study successfully executed a comprehensive numerical comparative analysis utilizing the PLAXIS 3D Finite Element Method to rigorously investigate the structural efficacy of integrating internal steel rings as a novel strategy for optimizing TBM segmental linings. The investigation provided quantitative evidence that the 25 cm thin segments, when reinforced with strategically placed steel rings, achieve structural performance levels comparable to, or even superior to, conventional 40 cm thick unsupported segments under challenging rock mass and high overburden conditions. The primary structural benefit stems from the superior load redistribution mechanism: the steel rings effectively manage and absorb substantial N\u003csub\u003e2\u003c/sub\u003e axial forces, consequently reducing the critical M\u003csub\u003e11\u003c/sub\u003e bending moments and flexural demands on the concrete elements. This enhancement in load transfer is robustly validated by the N-M interaction analysis, which confirmed that the loading points for the thin, reinforced segments fall well within the ultimate capacity curve, thereby maintaining a significant structural safety margin. The design innovation yields tangible economic and environmental advantages, translating directly into an approximate 43.7% reduction in concrete volume per linear meter of the tunnel, which not only lowers material costs but also reduces the necessary excavation diameter and streamlines logistics. In conclusion, the strategic use of steel rings represents a validated, performance-based approach for achieving material optimization in TBM tunnel design without compromising safety, paving the way for more economical and sustainable underground infrastructure projects.\u003c/p\u003e \u003cp\u003eWhile this study provides valuable insights, it is important to acknowledge certain limitations and identify areas for future research. The results are limited to the chosen soil type and valid for a certain behaviour for segment joints and specific steel ring configuration. Moreover, the current analysis is static and dynamic loads (e.g., seismic), long-term creep, shrinkage, and ground-structure interaction over extended periods are not considered.\u003c/p\u003e \u003cp\u003eFuture work should focus on the parametric optimization of ring design (spacing and cross-sectional geometry), investigation of long-term and dynamic load effects, and full-scale experimental validation to further enhance the practical applicability of this innovative system. Also, a detailed economic analysis, integrating the costs of materials, installation, and long-term maintenance, would be beneficial to fully quantify the economic advantages of steel ring integration.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting Interests\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eC.\u0026Ccedil;.: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data Curation, Writing - Original Draft, Writing - Review \u0026amp; Editing, Visualization.B.U.: Conceptualization, Methodology, Resources, Writing - Review \u0026amp; Editing, Supervision, Project administration.C.G.: Conceptualization, Validation, Investigation, Writing - Review \u0026amp; Editing. All authors have read and agreed to the published version of the manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets generated and analyzed during the current study (specifically the PLAXIS 3D numerical models and extracted structural force data) are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eGong, Q., Yin, L., Ma, H. \u0026amp; Zhao, J. TBM tunnelling under adverse geological conditions: An overview. \u003cem\u003eTunn. Undergr. 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Available: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://ir.lib.uwo.ca/etdhttps://ir.lib.uwo.ca/etd/1865\u003c/span\u003e\u003cspan address=\"https://ir.lib.uwo.ca/etdhttps://ir.lib.uwo.ca/etd/1865\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8554968/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8554968/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe escalating demands of global urbanization necessitate efficient and robust underground construction methods, with Tunnel Boring Machines (TBMs) being the predominant choice. The long-term performance of these projects heavily relies on the efficacy and structural reliability of precast concrete segmental lining systems. Despite their advantages, these linings are susceptible to critical structural weaknesses, such as high stress concentrations at joints and excessive deformations in challenging ground conditions. While reducing segment thickness offers sufficient economic and environmental benefits (material saving and reduced excavation diameter), it inherently compromises structural stiffness and safety margins. This study investigates the potential of internal steel rings as a supplementary reinforcement strategy to enhance the mechanical performance of thinner segmental linings, drawing conceptual inspiration from the successful application of steel support systems in the New Austrian Tunnelling Method (NATM). A comprehensive numerical comparative analysis was conducted using the PLAXIS 3D Finite Element Method under challenging rock mass and high overburden conditions. Three distinct tunnel lining models were simulated: a 25 cm reinforced concrete segment lining (Model 1), a 40 cm reinforced segment lining (Model 2), and a 25 cm reinforced concrete segment lining with strategically placed steel rings (Model 3). The analysis focused on Key Performance Indicators (KPIs), including total deformation, N\u003csub\u003e2\u003c/sub\u003e axial forces, Q\u003csub\u003e12\u003c/sub\u003e shear forces, and M\u003csub\u003e11\u003c/sub\u003e bending moments, and validated the structural safety using N-M interaction curves. The results demonstrate that the integration of steel rings successfully promotes a more favourable redistribution of internal forces, significantly reducing the critical bending moment M\u003csub\u003e11\u003c/sub\u003e demands on the concrete segments. Crucially, the numerical findings confirm that thinner 25 cm segments, when supported with steel rings, achieve structural performance levels comparable to, or even superior to, conventional thicker 40 cm segments, while maintaining a substantial safety margin as verified by the N-M interaction diagrams. This research validates a structurally robust and logistically efficient approach for material optimization, offering considerable potential for both economic and structural improvements in TBM tunnel design and aligning strongly with sustainable construction principles.\u003c/p\u003e","manuscriptTitle":"A Novel Approach for the Optimization of Segmental Linings in TBM Tunnels through Steel Ring Reinforcement","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-16 19:52:14","doi":"10.21203/rs.3.rs-8554968/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"4625bf57-f31c-493d-9cdd-06058e5a3db3","owner":[],"postedDate":"January 16th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":61212604,"name":"Physical sciences/Engineering"},{"id":61212605,"name":"Physical sciences/Materials science"}],"tags":[],"updatedAt":"2026-05-19T06:56:21+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-16 19:52:14","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8554968","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8554968","identity":"rs-8554968","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}