Investigation on the strain energy release prior to a major ground collapse of a large section soft rock tunnel

Investigation on the strain energy release prior to a major ground collapse of a large section soft rock tunnel | 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 Research Article Investigation on the strain energy release prior to a major ground collapse of a large section soft rock tunnel ALLOUACHE Abdelaziz N This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7312555/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 In this study, the surrounding ground mass energy release was investigated to demonstrate the inefficiency of the support system prior to a major ground collapse in a twin freeway tunnel excavated in a soft surrounding rock mass (with poor mechanical properties) using simulation. Unlike hard rocks, soft rocks tend to soften in the immediate vicinity of the underground excavation, as demonstrated in this case by a nodal output. Through dynamic analysis, it has been proven that the ground energy release has exceeded the energy provided by the support system, and the countermeasure support has a limited safety margin despite supplying sufficient energy. A feedback approach is proposed through a change in the excavation method, which has proven to be an efficient way to reduce ground energy release during the tunnel excavation process. Civil Engineering Geology Energy release ground collapse dynamic analysis soft rock tunnel FEA simulation 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 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20 Figure 21 Figure 22 Figure 23 Highlights This paper aims to provide an approach to the back analysis by investigating the released strain energy release prior to a major ground collapse of a soft rock tunnel In contrast with hard rocks, the energy release is lower at the immediate vicinity of the cavity The released energy is compared with those of the initially adopted support and the upgraded support, where an inefficiency has been pointed out The main issue is identified as being the excavated section rather than the support performance according to the collected results. The results outcomes show a good potential of reproducibility in the engineering problems. 1. Introduction In contrast to hard rocks, soft rocks tend to soften in the immediate vicinity of the tunnel's roof, resulting in stress loosening and energy release. Complex geological conditions increase the risks in tunnel construction, making it highly susceptible to collapses, large deformations, and other accidents, resulting in economic and human injuries [ 1 ]. In recent years, numerical simulation has emerged as a significant research technique that can determine the stress and displacement fields in both undisturbed and disturbed rock masses [ 2 , 3 ]. The primary challenge in the numerical analysis of surrounding rock deformation lies in investigating the engineering geological conditions, determining rock mass parameters, and selecting a suitable constitutive model to predict the trends of surrounding rock deformation. This method is typically used alongside field measurements [ 4 – 7 ]. The engineering analogy approach involves analyzing the governing factors and causal relationships affecting tunnel deformation and then developing corresponding correlations. Further analysis of the geological conditions of the tunnel under consideration, combined with functional correlations, is employed to predict tunnel deformation [ 8 – 10 ]. The numerical analysis of tunnel surrounding rock deformation is performed through theoretical methods, such as elastoplastic mechanics, and developing solutions for the deformation of the tunnel surrounding rock. This method has high theoretical reliability; however, its application is relatively complicated due to complex geological conditions [ 11 – 14 ]. Numerical simulation remains an effective way to investigate the evolutionary process of rock deformation and failure in deep tunnels, with advantages of flexibility and strong adaptability. The key points of numerical simulation are (1) utilizing appropriate numerical methods, including finite element, finite difference, discrete element, and coupled methods; (2) simulating the actual excavation and stress path, which includes simulating the unloading mode and unloading rate, such as the TBM method and blasting and drilling (D&B) method; (3) employing the constitutive model that can accurately describe the mechanical behavior of deep hard/soft rock. Moreover, tunnel excavation is a typical spatio-temporal evolution process with evident spatial constraint effects at the excavation face [ 15 ], and stress is not instantly released after unloading. The issue of stress release rate must be considered when using time-independent models, while time-dependent models can address this problem. Thus, creep models have been extensively used to analyze the mechanical behavior of surrounding rock in soft rock strata [ 16 – 18 ], but creep models and time-dependent stability indices can describe internal energy dissipation. This study aims to investigate the energy release of the tunnel's surrounding ground mass using numerical modeling with dynamic analysis, while a static analysis conducted in previous research (Allouache et al. 2025) serves for model validation. The tunnel at Djebel Ouahch, Constantine, located in the northeast of Algeria, is taken as a reference case. For feedback contribution, both static and dynamic analyses were performed to explore energy dissipation in another excavation method, namely the three-bench method (crown, stross, and invert). The dynamic and static analyses were carried out respectively using Abaqus and PLAXIS V22 software, with perfect elastoplastic and hardening soil constitutive models respectively. The results are expected to provide additional knowledge of the energy evolution process in soft rock tunnels. 2. Project overview The tunnel of "Djebel Ouahch," located in Algeria's Constantine province, serves as the benchmark for this research study. This tunnel is a section of the Maghreb Unity Highway (AUM, acronym in French). It spans around 700 km in length, traversing Algeria with an overall distance of 1,200 km. It crosses the Djebel Ouahch Mountain in northeastern Algeria, situated in the Constantine province, ranging from pk205 + 393 to pk207 + 384.5 ("pk" denotes a French term for kilometric point), totaling a length of 1,909 m. It consists of a twin-tunnel with a radius of 9.57 m, positioned 17 m apart from one another. The typical depth is approximately 120 m, with a local maximum of 140 m, whereas the thinnest coverage is 12 m, featuring an area nearing 190 m² in the form of a lowered vault, illustrated in Fig. 2 . Based on the reconnaissance campaign conducted, both tunnels have consistently intersected the marl-limestone zone linked to the Tellian layer, especially within the Cretaceous argillite unit. Quaternary colluviums seem to appear locally at the surface. Rough colluviums consist of heterogeneous sandstone components, pebbles, and angular boulders with red silty matrix, as illustrated in Fig. 3 . On January 1, 2014, from 16:00 to 16:30, a significant ground subsidence took place in the left tunnel, spanning from mileage pk206 + 150 to pk206 + 280 (with "pk" being a French abbreviation for kilometric point). The collapse significantly harmed the right tube (which was already finished and operational at that time), inflicting serious harm to the lining of the right tube, with the total length of the collapse reaching 140 m. No injuries or fatalities were reported after the incident. In the construction documentation, both tunnels have been dug utilizing the identical procedure. The right tube has been fully excavated and is operational; thereafter, the second tube (left tube) was constructed. The NATM (New Austrian Tunnelling Method) was employed in the construction of the left tube, using the bench-cut excavation approach. A two-tiered support structure was utilized during the construction phase of the left tunnel. The materials for the temporary support scheme included HEB 200 steel arches with a pitch spacing of 0.75 m, 6 m long hollow micro-fissured fiberglass bolts, and a 30 cm thick layer of shotcrete. A 60 cm thick layer of reinforced concrete was utilized for the secondary lining. 3. Methodology First, the support energy will be determined by a generalized energy model under the action of original support, as shown in Fig. 5 . A large amount of elastic energy is accumulated under the influence of geo-stress (spring compression, Fig. 5 (a)) during the non-excavation stage of the surrounding rock. After excavating the surrounding rock, energy is released (spring elongation), accompanied by a series of energy dissipation losses, such as plastic dissipation (sliding friction, Fig. 5 (b)). When the energy is released to a certain extent and reaches a new energy balance point, the surrounding rock becomes stable. In the anchoring reinforcement support model, the excavation energy of the surrounding rock is released to a certain extent for reinforcement support. The energy absorbed by the original support and the anchor reinforcement support in the energy balance stage forms a new balance system with the release of energy from the rock mass. It is pertinent to note that reinforcement support should be carried out before the unstable stage. Assuming that in the original support state, the total energy released by the surrounding rock to the outside is W_total, and the displacement of the slider is x_0, as suggested by Eq. (1). W total = F spring *x 0 Eq. (1) The support system is made of HEB-200 steel-arch profile and a 30 cm shotcrete layer. Prior to the collapse, an upgraded support system was adopted by doubling the HEB-200 profiles, and apply an additional 25 cm shotcrete layer. The support maximum pressure and maximum deformation were calculated according to the Hoek & Brown (1980) [ 20 ] rock-support interaction approach. Table 1 sums up both HEB profiles and shotcrete characteristics. Table 1 Support characteristics HEB-200 profiles Shotcrete Young modulus 210000 MPa 30000 MPa Moment of inertia 0.00057 m 4 0.0036 m 4 Resistance of the material 410 MPa 30 MPa Spacing 0.75 m / Thickness / 0.3 m Cross-section 0.0781 m² / Poisson’s ration 0.2 0.2 According to rock-support interaction method proposed by Hoek & Brown (1980), the pressure of the steel (Psmax) and shotcrete (Pcmax) elements give: Psmax = 0.220105 MPa Pcmax = 1.077115 MPa. The combined support pressure is made by the addition of both pressure, hence the maximum pressus (Pmax) gives us: Pcmax = Psmax + Pcmax = 1.29722. The countermeasure support scheme first shotcrete layer is of 35 cm, and the second shotcrete layer is of 25 cm, so the updated support pressure (Pmax-2) gives us: Pmax-2 = 2.290787 MPa. Umax-1 and Umax-2 are the maximum deformations of both support scheme calculated by the same method. Umax-1 = 0.00366536 m, and Umax-2 = 0.003396509 m The Table 2 recapitulates the total work of both support schemes according to Eq. (1). The force is calculated by dividing the maximum pressure on the steel section, assuming of course that the force is applied perpendicularly to the same plane. Table 2 Provided energy by the support systems Support system Provided energy (J) Initial support system 60541.8 Upgraded support system 99624.57 3.1. Dynamic analysis Based on a 2D FEA model conducted using Abaqus with a dynamic/explicit solver to identify failure phenomena with a plastic behavior constitutive model, a nodal output is considered to effectively identify the inefficiency of the initially used support. The model geometry is 200 m long and 200 m deep, with a free mesh using a medial axis algorithm composed of 1,849 quadratic elements, as shown in Fig. 6 . Two nodes were selected for output: the first at the crown of the tunnel in the immediate vicinity of the cavity, and a second at the upper vicinity of the excavation as shown in Fig. 7 . The distance between both nodes is equal to that between two discretized elements, i.e., 2 m. The rock-burst phenomenon tends to accumulate energy, followed by a sudden release. Conversely, in ground with poor mechanical properties, the rock mass tends to loosen around the cavity. A perfect elasto-plastic model represents the behavior model in this case. An increase in plasticity can clearly reproduce the behavior in a plastic regime, with the loading accounted for by gravity loading. The parameters of the behavior are summarized in Table 3 . Table 3 Behaviour constitutive model used for the simulation Young modulus (MPa) Poisson’s ratio Yield stress (KPa) Plastic strain (%) Unit weight (KN/m 3 ) 200 0.3 605 0 / / 605 1.25 24 / / 605 2.8 / / 605 4.5 3.2. Feedback contribution In Section 4 ( Results & Discussions ), it was found that the energy release exhibits substantial values. For this reason, a feedback contribution is proposed through a three-bench excavation method. This method is modeled using dynamic analysis with Abaqus FEA software, employing the same methodology mentioned earlier. A static analysis has also been carried out using PLAXIS V22 FEA software with the three-bench excavation method. From the proposed approach illustrated in Fig. 3 , the energy output in PLAXIS is determined by the forces applied to the plate elements and the vertical phase displacements registered during the bench excavation. The Abaqus models in the feedback contribution share the same boundaries as the first model. The only difference is that the first model is created by excavating the crown first, while the second is modeled by excavating both the crown and the middle bench using the same meshing procedure, i.e., a free quadratic mesh with a medial axis algorithm, where the number of elements is 2028 and 1852, respectively, as shown in Figs. 8 and 9 . The PLAXIS 2D model is 250 m long and 230 m deep, featuring a fine mesh with 962 elements and 7973 nodes, as indicated in Fig. 10 . The loading is also considered as gravity, with the "Hardening Soil Model " adopted as the constitutive model. Tables 4 and 5 summarize the characteristics of the constitutive model and the lining material used for the simulation, respectively. Table 4 Constitutive model used in PLAXIS modelling E50ref (MPa) 400 Eoed ref (MPa) 400 Eur ref (MPa) 825 ν ur 0.2 Power “m” 0.5 Pref (MN) 0.1 C (MN) 0.2 Φ° 24 Table 5 Lining material used for PLAXIS modelling Properties and units Lining material Invert material Material type Elastic Elastic Linear weight (KN/m/m) 10 6.3 Axial stiffness (KN/m) 8.33E6 3.75E6 Bending stiffness (KN.m²/m) 92.38E3 19.35E3 Poisson’s ratio 0.2 0.2 4. Results and discussions 4.1. Dynamic analysis results Figure 11 and 12 show the evolution of the energy release at the higher node (node 277, as indicated in Fig. 7 ) in both shear and compression components respectively S12 and S22. Sudden energy release is observed with magnitudes broadly superior compared to the energy of the initial support scheme. First, the original equilibrium is mainly in triaxial state, then disturbed with the presence of the cavity, which renders the problem in a bi-axial state. Failures are registered twice, in early and delayed failures, where both values of the early failure (i.e. 67576,43J) and delayed failure (-71610,41J & -69696,93J) are superior to the energy of the initial support system (see Table 2 .). In Fig. 12 , with compression component, the early failure (at 1& 2 with magnitudes reaching − 83291,7J & -83005,12 respectively) are still superior to the initial support system as well as with the delayed failure (-76056,43J). With the malfunction of the first support resulting in considerable deformations, the upgraded support system may not react properly or has a reduced margin than initially accounted for the presented situation. The Figs. 13 and 14 show the nodal output of the node 15 (see Fig. 7 .) in shear and compression components respectively. The nodal output of the lower node in both shear and compression exhibits values significantly lower than the energy magnitude of the initial support scheme. In the direct contour of the excavation, the surrounding ground experiences a loosening pressure due to the energy release exerted initially. The recorded fluctuations in these curves are caused by iterative calculations and do not affect the analysis of the overall evolution law. Clearly, it can be observed that the SED of the surrounding rock at the tunnel wall shows a downward-upward-downward trend. When critical stress is reached, accumulated strain energy is released abruptly, leading to a drop in stored energy and stress, forming the " saw tooth" like curves. In the compression component (S22), the respective downward and upward movements are due to crack increase and crack closing (recovery and rise in crack closing), whereas in the shear component, the downward movement is due to crack increase and the upward trend results from crack closing with a positive value, which is synonymous with a tensile effect (lateral extent). This behavior is a result of an initial increase in strain energy as the load is applied to the cavity, followed by a sudden drop when a segment of crack jumps through a weak interface, then recovery and rise occur as cracks close or slow down in a harder portion. Near the excavation face, the three principal stresses of the rock mass decrease under the unloading effect of excavation, causing the decline and initial release of SED. In the tunnel section, the surrounding rock of the tunnel crown begins the stress redistribution evolution process under a biaxial stress state, and the stress continuously concentrates until reaching biaxial strength, leading to the accumulation and concentration of strain energy [ 21 ]. In previous research conducted by the authors [ 19 ], the left tunnel, prior to the collapse phenomenon, was undergoing a significant decompressed area extending up to a height of 40 m above the crown of the tunnel, established by numerical modeling with the relative shear stress component. The output was validated by the geophysical reconnaissance campaign, as demonstrated in the earlier research work. 4.2. Feedback contribution with dynamic analysis As suggested in the methodology section, considering the tunnel section as well, a feedback approach is proposed by changing the excavation technique given the amount of energy release recorded in section 4.1. The change in the excavation method has contributed to a decrease in the released energy, where the slower excavation pace registered the safest energy release in this case. In the part where the crown is excavated first, node 277 became node 21, and in the part where the crown and middle bench are excavated, the node designation will be node 187 (see Fig. 7). Figures 16 and 17 show the energy evolution in the considered node with the shear and compression components, considering the crown excavation only. Both Figs. 16 and 17 show a clear decrease in energy when the crown of the tunnel is excavated on its own; the peak energy releases are recorded at 50,148 J in compression and 52,480 J, which is a lower value compared to the initial support scheme (see Table 2 ). The displacements should normally decrease with the reduction of the excavated section, leading to a more gradual release of strain energy, which provides a sufficient margin for reaction during the excavation process compared to a larger section, considering the poor mechanical properties of the surrounding rock where the tunnel is excavated. Figure 18 and 19 show the energy evolution in the considered node, including the shear and compression components, when both the crown and the middle bench are excavated. In a more critical section, the stress redistribution is higher, resulting in a greater energy release during excavation. In this case, peaks are recorded at 80015.3 J and 69318.37 J in the compression and shear components, respectively. These values exceed the provided energy of the initial support scheme but remain below the maximum provided energy from the upgraded support system. However, in the compression component, the exhibited value has a closely critical safety margin (with a margin of 19.67%). During the construction phase, the surrounding ground experiences time -dependent degradation, as the tunneling process has an evident temporal-dimensional effect [ 22 , 23 ]. 4.3. Feedback contribution with static analysis The static analysis has been carried out using PLAXIS V22 with 2D plane strain analysis. The modeling methodology is described in Section 3.2, the input data are detailed in Tables 4 and 5 , and the mesh is shown in Fig. 10 . Figures 20 and 21 respectively show the vertical phase displacements and the applied axial force for the crown and middle bench excavation methods. With the recorded 0.046 m vertical displacements and the applied axial forces on the plates of 1392 KN, the calculated energy should then be 64032 J by this proposed method. The Figs. 22 and 23 respectively show the vertical phase displacements and the applied axial force respectively for the crown excavation only. With the recorded 0.07 m vertical displacements and the applied axial forces on the plates of 1358 KN, the calculated energy should then be 93702 J by this proposed method. The results output can seem a bit confusing since the lower excavation section exhibits higher energy in the output; however, in the stability analysis, during the excavation of the crown, there is a deadweight that has been released at the level of the roof, making the crown of the tunnel more prone to instabilities during tunneling, especially if this part of the tunnel is excavated first. When the excavation of the crown and the middle bench is carried out, the stress redistribution is also applied to the sidewalls of the tunnel, which somewhat alleviates the additional stress endured on the roof. Other excavation methods can also be proposed to mitigate the risks related to tunnel excavation. 5. Conclusion In this study, an investigation of the strain energy evolution has been carried out using numerical simulations in both dynamic and static cases prior to a ground collapse in a large section soft rock tunnel due to insufficient support performance. Through finite element analysis (FEA) dynamic analysis, it was demonstrated that the initial support could no longer withstand the surrounding rock reaction due to the excavation process, as indicated by nodal output at the crown of the tunnel in compression and shear components, where the support failed to provide sufficient energy to counteract the ground reaction. Moreover, the countermeasure support exhibited adequate energy compared to the ground reaction, but not with a broad safety margin, which may compromise the integrity of the infrastructure in the long term. At a certain point, changing and/or upgrading the support system does not necessarily yield the expected performance; the ground reaction must be anticipated according to the stress release rather than the applied support capacity, so as to increase the rock mass bearing capacity. For practical purposes, altering the excavation process is the best solution to adopt, given that the surrounding ground will react excessively and that the support, even if it provides sufficient pressure, may undergo time-dependent deformation that could affect its performance. In the static analysis, a typical solution for stability analysis is provided, where the plate elements undergo energy release. From this perspective, the analysis showed a limit equilibrium where the energy release was less than the energy provided by the countermeasure support but with a low safety margin, which may lead to a critical situation during the tunneling process. By altering the excavation process, the released energy decreased due to the reduction in section size but remained significant at the crown of the tunnel due to the deadweight effect on the tunnel roof. Declarations Acknowledgment Authors express their deep gratitude for granting access to the construction yard, as well as their accompanying during the internship of the first author. Authors are also thankful to the responsible society of the constructions for their help and providing the necessary data for this work’s fulfilment. Authors’ contribution Allouache Abdelaziz N : Conceptualization, Data acquisition, Investigation, Data curation, Formal analysis, Methodology, Plaxis Software, Supervision, Validation, Original draft. Bensehamdi Salim : Data curation, Formal analysis, Investigation, Project administration, Supervision, Visualisation, review & editing. Nettour Djamel : Supervision, Visualization, Review & editing. Saurabh Kureel : Abaqus software, Supervision, Review & editing. Funding This work did not receive any funding, or any specific grant from any part of any kind. Competing interest Authors of this work declare that there are no competing interests, conflicts, or any related conflicts of interests from any part of any kind AI use declaration The authors used AI assistance for a grammar check purpose (link: https://www.zerogpt.com/) During the preparation of this work the authors used “Zero GPT” AI tool (link: https://www.zerogpt.com) in order to check the grammar and spelling. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication. References Li G, Luo Z, Wu C, Lu H (2024) C. Zhu Integrated early warning and reinforcement support system for soft rock tunnels: a novel approach utilizing catastrophe theory and energy transfer laws Tunn Undergr Space Technol, 150 Article 105869. 10.1016/j.tust.2024.105869 Cai WQ, Zhu HH, Liang WH (2022a) Three-dimensional tunnel face extrusion and reinforcement effects of underground excavations in deep rock masses. Int J Rock Mech Min Sci 150:104999 Cai WQ, Zhu HH, Liang WH (2022b) Three-dimensional stress rotation and control mechanism of deep tunneling incorporating generalized ZhangeZhu strength-based forward analysis. Eng Geol 308:106806 Li G, Ma F, Guo J, Zhao H (2021b) Case study of roadway deformation failure mechanisms: Field investigation and numerical simulation. Energies 14:1032 Li J, Hu M, Ding E, Kong W, Pan D, Chen S (2016) Multi-parameter numerical simulation of dynamic monitoring of rock deformation in deep mining. Int J Min Sci Technol 26:851–855 Sakcali A, Yavuz H (2019) Estimation of radial deformations around circular tunnels in weak rock masses through numerical modelling. Int J Rock Mech Min Sci 123:104092 Song Z, Yang T, Jiang A, Zhang D, Jiang Z (2016) Experimental investigation and numerical simulation of surrounding rock creep for deep mining tunnels. J South Afr Inst Min Metall 116:1181–1188 Bai C, Xue Y, Qiu D, Su M, Ma X, Liu H (2021) Analysis of factors affecting the deformation of soft rock tunnels by data envelopment analysis and a risk assessment model. Tunn Undergr Space Technol 116:104111 Liu W, Chen J, Chen L, Luo Y, Shi Z, Wu Y (2022) Nonlinear deformation behaviors and a new approach for the classifcation and prediction of large deformation in tunnel construction stage: a case study. Eur J Environ Civ Eng 26:2008–2036 Xue Y, Zhang X, Li S, Qiu D, Su M, Li L, Li Z, Tao Y (2018) Analysis of factors influencing tunnel deformation in loess deposits by data mining: a deformation prediction model. Eng Geol 232:94–103 Parsapour D, Fahimifar A (2016) Semi-analytical solution for time-dependent deformations in swelling rocks around circular tunnels. Geosci J 20:517–528 Xiaolin C, Weiming G, Fengxi Z, Guoliang D (2019) Stress analytical solution for shallow buried lined circular tunnel under the deformation of surrounding rock inner edge. Geotech Geol Eng 37:3771–3780 Yang Z, Xu J, Feng Q, Liu W, He P, Fu S (2022) Elastoplastic analytical solution for the stress and deformation of the surrounding rock in cold region tunnels considering the influence of the temperature feld. Int J Geomech 22:04022118 Zareifard MR, Fahimifar A (2016) Analytical solutions for the stresses and deformations of deep tunnels in an elastic-brittle-plastic rock mass considering the damaged zone. Tunn Undergr Space Technol 58:186–196 Sun C, Chen DX, Wang LG et al (2021) Quantitative evaluation of the constraint effect and stability of tunnel lining support. Tunn Undergr Space Technol 112:103920 Leone T, Nordas AN, Anagnostou G (2023) Effects of Creep on Shield Tunnelling Through Squeezing Ground. Rock Mech Rock Eng Xu GW, Gutierrez M, Arora K et al (2022) Visco-plastic response of deep tunnels based on a fractional damage creep constitutive model. Acta Geotech 17:613–633 Zhang JB, Du RH, Zhang XH et al (2023) Experimental and numerical investigation of the rheological characteristics of tunnels in cold regions during excavation and operation. Acta Geotech ALLOUACHE AN, Bensehamdi S, Hrubesova E et al (2025) Geomechanical Back Assessment of a Major Ground Collapse of a Twin Tunnel located in the Eastern Section of the Algerian Highway. Indian Geotech J. https://doi.org/10.1007/s40098-025-01177-8 Hoek E, Brown ET (1980) Underground Excavations in Rock. London. Institution of Mining Metallurgy. https://doi.org/10.1201/9781482288926 Liu Y, Zhang R, Hou S et al (2025) Investigation of energy evolution process of rock mass during deep tunnel excavation based on elasto-viscoplastic damage model and time-dependent energy indices. Acta Geotech 20:1549–1570. https://doi.org/10.1007/s11440-024-02485-8 Aydan O¨, Akagi T, Kawamoto T (1993) The squeezing potential of rocks around tunnels: theory and prediction. Rock Mech Rock Eng 26:137–163 Singh M, Singh B, Choudhari J (2007) Critical strain and squeezing of rock mass in tunnels. Tunn Undergr Space Technol 22(3):343–350 Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7312555","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":496772634,"identity":"b6fb5b17-a57a-4dbd-bf04-659904422d84","order_by":0,"name":"ALLOUACHE Abdelaziz N","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0007-7638-6770","institution":"National higher school of technology and engineering","correspondingAuthor":true,"prefix":"","firstName":"ALLOUACHE","middleName":"Abdelaziz","lastName":"N","suffix":""}],"badges":[],"createdAt":"2025-08-06 19:09:10","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7312555/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7312555/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":88646593,"identity":"d36b4855-9fb0-4892-ac9c-4a556f464152","added_by":"auto","created_at":"2025-08-08 16:35:32","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1119524,"visible":true,"origin":"","legend":"\u003cp\u003eTunnel’s geographic location, T1 with red line\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/e47631c9638470c9d432979e.png"},{"id":88646557,"identity":"0e834de3-bf62-4ef5-9e24-4fb4e4de76bd","added_by":"auto","created_at":"2025-08-08 16:35:31","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":92753,"visible":true,"origin":"","legend":"\u003cp\u003eTunnel’s cross sections in “meter”\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/516bfbafe664ec3f7fc31f46.png"},{"id":88646591,"identity":"a966efc9-b901-4647-8c23-f5ef99a33363","added_by":"auto","created_at":"2025-08-08 16:35:32","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1086520,"visible":true,"origin":"","legend":"\u003cp\u003eCretaceous Argillite rock, which is the major surrounding rock constitution of the tunnel “T1”\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/69f3738f3221f02dc2d30cde.png"},{"id":88646562,"identity":"896018b7-9b7d-4016-a8c8-06f14bfd0d59","added_by":"auto","created_at":"2025-08-08 16:35:31","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":841558,"visible":true,"origin":"","legend":"\u003cp\u003eCollapse phenomenon occasioned damages\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/a71308f7dc4f23c4ea3f2391.png"},{"id":88647707,"identity":"9fe477fb-b2b7-4367-8db4-7c1fddf6003a","added_by":"auto","created_at":"2025-08-08 16:51:31","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":89413,"visible":true,"origin":"","legend":"\u003cp\u003eGeneralized energy model under the action of support system reinforcement [1]\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/7d7544ebf926d650979e16b6.png"},{"id":88647464,"identity":"43d2499d-4371-41e1-98ae-07d14fb86641","added_by":"auto","created_at":"2025-08-08 16:43:32","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":164399,"visible":true,"origin":"","legend":"\u003cp\u003eModel mesh and boundary\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/638bb7fd99d3a1b6ad12ed9a.png"},{"id":88646626,"identity":"66554258-5528-403c-b9ce-fd06979c5e15","added_by":"auto","created_at":"2025-08-08 16:35:33","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":298213,"visible":true,"origin":"","legend":"\u003cp\u003eNodes considered for the computation output\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/4e2fc690dcf129a3fb6c6fb6.png"},{"id":88646551,"identity":"acfcf1a0-d5c6-40e1-acd8-263433537510","added_by":"auto","created_at":"2025-08-08 16:35:30","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":172954,"visible":true,"origin":"","legend":"\u003cp\u003eCrown excavation method mesh\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/4037bb21a2eda7199e545258.png"},{"id":88647455,"identity":"dc7ac09c-0e4e-46b9-8949-e68c91210c2c","added_by":"auto","created_at":"2025-08-08 16:43:31","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":164436,"visible":true,"origin":"","legend":"\u003cp\u003eCrown and middle bench excavation mesh\u003c/p\u003e","description":"","filename":"image9.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/04e25dbfc3b713b1db42cbea.png"},{"id":88647450,"identity":"4431a9ed-8486-4804-bf19-9afd34d87dc6","added_by":"auto","created_at":"2025-08-08 16:43:30","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":219861,"visible":true,"origin":"","legend":"\u003cp\u003ePLAXIS mesh used for modelling\u003c/p\u003e","description":"","filename":"image10.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/dafb15395cf7896c40951f40.png"},{"id":88647466,"identity":"c891420e-4c25-43d6-bedb-0e07e45cc8d6","added_by":"auto","created_at":"2025-08-08 16:43:33","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":170268,"visible":true,"origin":"","legend":"\u003cp\u003eNodal output of the strain energy in the shear component of the node 277\u003c/p\u003e","description":"","filename":"image11.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/fee9e453f947df26bb56cbd1.png"},{"id":88646608,"identity":"aa2984da-99c1-4efa-a656-23cca8b240eb","added_by":"auto","created_at":"2025-08-08 16:35:33","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":159310,"visible":true,"origin":"","legend":"\u003cp\u003eNodal output of the strain energy in the compression component of the node 277.\u003c/p\u003e","description":"","filename":"image12.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/e7699fd4d283a11cebec79f9.png"},{"id":88647453,"identity":"4dfa2bc3-f061-4ef0-8909-2dbd5e2d476f","added_by":"auto","created_at":"2025-08-08 16:43:31","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":117900,"visible":true,"origin":"","legend":"\u003cp\u003eNodal output of the strain energy in the shear component of the node 15.\u003c/p\u003e","description":"","filename":"image13.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/2f34e21a1ae22967b26db03a.png"},{"id":88646599,"identity":"ec12fbfa-bf75-4da1-9663-1e594c735666","added_by":"auto","created_at":"2025-08-08 16:35:32","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":115938,"visible":true,"origin":"","legend":"\u003cp\u003eNodal output of the strain energy in the compression component of the node 15.\u003c/p\u003e","description":"","filename":"image14.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/e0ff4e644b3a7e892bba8537.png"},{"id":88646632,"identity":"ee1cba61-8ac4-427e-bcc7-df137fc67f34","added_by":"auto","created_at":"2025-08-08 16:35:34","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":208893,"visible":true,"origin":"","legend":"\u003cp\u003eDecompressed area underwent by the left tunnel prior to the collapse [19]\u003c/p\u003e","description":"","filename":"image15.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/16abc9adefd82be60100ef89.png"},{"id":88647473,"identity":"125abb9c-085c-47a5-8ed2-f01f439cec03","added_by":"auto","created_at":"2025-08-08 16:43:34","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":50481,"visible":true,"origin":"","legend":"\u003cp\u003eNodal output of the strain energy in shear component of node 21 during the crown excavation.\u003c/p\u003e","description":"","filename":"image16.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/f7c9f20e2f7247e9a4962b42.png"},{"id":88646554,"identity":"b37ec21e-e80d-413d-8d93-6d8c3016ab87","added_by":"auto","created_at":"2025-08-08 16:35:30","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":56018,"visible":true,"origin":"","legend":"\u003cp\u003eNodal output of the strain energy in compression component of node 21 during the crown excavation.\u003c/p\u003e","description":"","filename":"image17.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/cb3e636934971a6fa517eb7a.png"},{"id":88646609,"identity":"865cb547-98ab-42dc-a566-2694e5fd9fb6","added_by":"auto","created_at":"2025-08-08 16:35:33","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":51710,"visible":true,"origin":"","legend":"\u003cp\u003eNodal output of the strain energy in shear component of node 187 during the excavation of the crown and the middle bench.\u003c/p\u003e","description":"","filename":"image18.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/3d236a58c4e39b88bad0bdc3.png"},{"id":88647465,"identity":"42e306a3-f0f0-4198-892c-ad5691394fb0","added_by":"auto","created_at":"2025-08-08 16:43:33","extension":"png","order_by":19,"title":"Figure 19","display":"","copyAsset":false,"role":"figure","size":60625,"visible":true,"origin":"","legend":"\u003cp\u003eNodal output of the strain energy in compression component of node 187 during the excavation of the crown and the middle bench.\u003c/p\u003e","description":"","filename":"image19.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/d3369a35ebfc6318cf28522d.png"},{"id":88646631,"identity":"7e07a639-2de8-496c-8a4a-e89c36dd4a4c","added_by":"auto","created_at":"2025-08-08 16:35:34","extension":"png","order_by":20,"title":"Figure 20","display":"","copyAsset":false,"role":"figure","size":100851,"visible":true,"origin":"","legend":"\u003cp\u003eRecorded vertical phase displacements during the excavation of both crown and bench\u003c/p\u003e","description":"","filename":"image20.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/bc91b76c764eb56b60df76e9.png"},{"id":88647460,"identity":"68161582-b9e9-457d-a93f-e060b986fcd7","added_by":"auto","created_at":"2025-08-08 16:43:32","extension":"png","order_by":21,"title":"Figure 21","display":"","copyAsset":false,"role":"figure","size":81634,"visible":true,"origin":"","legend":"\u003cp\u003eApplied axial forces on the crown tunnel during the excavation of both crown and bench\u003c/p\u003e","description":"","filename":"image21.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/e5e036feefc177e784b2b9b7.png"},{"id":88646575,"identity":"1e18e00b-420b-46d7-b7df-8dcb3b8ef9f3","added_by":"auto","created_at":"2025-08-08 16:35:31","extension":"png","order_by":22,"title":"Figure 22","display":"","copyAsset":false,"role":"figure","size":97626,"visible":true,"origin":"","legend":"\u003cp\u003eRecorded vertical phase displacements during the excavation of the crown.\u003c/p\u003e","description":"","filename":"image22.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/6476fcc7cf67e0745ff1e992.png"},{"id":88646577,"identity":"40ec33fd-e9ec-49ec-8f20-ab8c4541c99c","added_by":"auto","created_at":"2025-08-08 16:35:31","extension":"png","order_by":23,"title":"Figure 23","display":"","copyAsset":false,"role":"figure","size":80775,"visible":true,"origin":"","legend":"\u003cp\u003eApplied axial forces on the crown tunnel during the excavation of the crown.\u003c/p\u003e","description":"","filename":"image23.png","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/3fc4b4d7e57566326bea5749.png"},{"id":88649145,"identity":"9010e2ad-b14e-4128-8a5e-e1e0832555b1","added_by":"auto","created_at":"2025-08-08 16:59:33","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5613228,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7312555/v1/b6815832-22e1-4d2f-aabd-9a04823c1f81.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eInvestigation on the strain energy release prior to a major ground collapse of a large section soft rock tunnel\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"Highlights","content":"\u003cul\u003e\n \u003cli\u003eThis paper aims to provide an approach to the back analysis by investigating the released strain energy release prior to a major ground collapse of a soft rock tunnel\u003c/li\u003e\n \u003cli\u003eIn contrast with hard rocks, the energy release is lower at the immediate vicinity of the cavity\u003c/li\u003e\n \u003cli\u003eThe released energy is compared with those of the initially adopted support and the upgraded support, where an inefficiency has been pointed out\u003c/li\u003e\n \u003cli\u003eThe main issue is identified as being the excavated section rather than the support performance according to the collected results.\u003c/li\u003e\n \u003cli\u003eThe results outcomes show a good potential of reproducibility in the engineering problems.\u003c/li\u003e\n\u003c/ul\u003e"},{"header":"1. Introduction","content":"\u003cp\u003eIn contrast to hard rocks, soft rocks tend to soften in the immediate vicinity of the tunnel's roof, resulting in stress loosening and energy release. Complex geological conditions increase the risks in tunnel construction, making it highly susceptible to collapses, large deformations, and other accidents, resulting in economic and human injuries [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. In recent years, numerical simulation has emerged as a significant research technique that can determine the stress and displacement fields in both undisturbed and disturbed rock masses [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe primary challenge in the numerical analysis of surrounding rock deformation lies in investigating the engineering geological conditions, determining rock mass parameters, and selecting a suitable constitutive model to predict the trends of surrounding rock deformation. This method is typically used alongside field measurements [\u003cspan additionalcitationids=\"CR5 CR6\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. The engineering analogy approach involves analyzing the governing factors and causal relationships affecting tunnel deformation and then developing corresponding correlations. Further analysis of the geological conditions of the tunnel under consideration, combined with functional correlations, is employed to predict tunnel deformation [\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe numerical analysis of tunnel surrounding rock deformation is performed through theoretical methods, such as elastoplastic mechanics, and developing solutions for the deformation of the tunnel surrounding rock. This method has high theoretical reliability; however, its application is relatively complicated due to complex geological conditions [\u003cspan additionalcitationids=\"CR12 CR13\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Numerical simulation remains an effective way to investigate the evolutionary process of rock deformation and failure in deep tunnels, with advantages of flexibility and strong adaptability. The key points of numerical simulation are (1) utilizing appropriate numerical methods, including finite element, finite difference, discrete element, and coupled methods; (2) simulating the actual excavation and stress path, which includes simulating the unloading mode and unloading rate, such as the TBM method and blasting and drilling (D\u0026amp;B) method; (3) employing the constitutive model that can accurately describe the mechanical behavior of deep hard/soft rock. Moreover, tunnel excavation is a typical spatio-temporal evolution process with evident spatial constraint effects at the excavation face [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], and stress is not instantly released after unloading. The issue of stress release rate must be considered when using time-independent models, while time-dependent models can address this problem. Thus, creep models have been extensively used to analyze the mechanical behavior of surrounding rock in soft rock strata [\u003cspan additionalcitationids=\"CR17\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], but creep models and time-dependent stability indices can describe internal energy dissipation.\u003c/p\u003e\u003cp\u003eThis study aims to investigate the energy release of the tunnel's surrounding ground mass using numerical modeling with dynamic analysis, while a static analysis conducted in previous research (Allouache et al. 2025) serves for model validation. The tunnel at Djebel Ouahch, Constantine, located in the northeast of Algeria, is taken as a reference case. For feedback contribution, both static and dynamic analyses were performed to explore energy dissipation in another excavation method, namely the three-bench method (crown, stross, and invert). The dynamic and static analyses were carried out respectively using Abaqus and PLAXIS V22 software, with perfect elastoplastic and hardening soil constitutive models respectively. The results are expected to provide additional knowledge of the energy evolution process in soft rock tunnels.\u003c/p\u003e"},{"header":"2. Project overview","content":"\u003cp\u003eThe tunnel of \"Djebel Ouahch,\" located in Algeria's Constantine province, serves as the benchmark for this research study. This tunnel is a section of the Maghreb Unity Highway (AUM, acronym in French). It spans around 700 km in length, traversing Algeria with an overall distance of 1,200 km. It crosses the Djebel Ouahch Mountain in northeastern Algeria, situated in the Constantine province, ranging from pk205\u0026thinsp;+\u0026thinsp;393 to pk207\u0026thinsp;+\u0026thinsp;384.5 (\"pk\" denotes a French term for kilometric point), totaling a length of 1,909 m.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIt consists of a twin-tunnel with a radius of 9.57 m, positioned 17 m apart from one another. The typical depth is approximately 120 m, with a local maximum of 140 m, whereas the thinnest coverage is 12 m, featuring an area nearing 190 m\u0026sup2; in the form of a lowered vault, illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eBased on the reconnaissance campaign conducted, both tunnels have consistently intersected the marl-limestone zone linked to the Tellian layer, especially within the Cretaceous argillite unit. Quaternary colluviums seem to appear locally at the surface. Rough colluviums consist of heterogeneous sandstone components, pebbles, and angular boulders with red silty matrix, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eOn January 1, 2014, from 16:00 to 16:30, a significant ground subsidence took place in the left tunnel, spanning from mileage pk206\u0026thinsp;+\u0026thinsp;150 to pk206\u0026thinsp;+\u0026thinsp;280 (with \"pk\" being a French abbreviation for kilometric point). The collapse significantly harmed the right tube (which was already finished and operational at that time), inflicting serious harm to the lining of the right tube, with the total length of the collapse reaching 140 m. No injuries or fatalities were reported after the incident.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIn the construction documentation, both tunnels have been dug utilizing the identical procedure. The right tube has been fully excavated and is operational; thereafter, the second tube (left tube) was constructed. The NATM (New Austrian Tunnelling Method) was employed in the construction of the left tube, using the bench-cut excavation approach. A two-tiered support structure was utilized during the construction phase of the left tunnel. The materials for the temporary support scheme included HEB 200 steel arches with a pitch spacing of 0.75 m, 6 m long hollow micro-fissured fiberglass bolts, and a 30 cm thick layer of shotcrete. A 60 cm thick layer of reinforced concrete was utilized for the secondary lining.\u003c/p\u003e"},{"header":"3. Methodology","content":"\u003cp\u003eFirst, the support energy will be determined by a generalized energy model under the action of original support, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. A large amount of elastic energy is accumulated under the influence of geo-stress (spring compression, Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a)) during the non-excavation stage of the surrounding rock. After excavating the surrounding rock, energy is released (spring elongation), accompanied by a series of energy dissipation losses, such as plastic dissipation (sliding friction, Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b)). When the energy is released to a certain extent and reaches a new energy balance point, the surrounding rock becomes stable. In the anchoring reinforcement support model, the excavation energy of the surrounding rock is released to a certain extent for reinforcement support.\u003c/p\u003e\u003cp\u003eThe energy absorbed by the original support and the anchor reinforcement support in the energy balance stage forms a new balance system with the release of energy from the rock mass. It is pertinent to note that reinforcement support should be carried out before the unstable stage. Assuming that in the original support state, the total energy released by the surrounding rock to the outside is W_total, and the displacement of the slider is x_0, as suggested by Eq.\u0026nbsp;(1).\u003c/p\u003e\u003cp\u003eW\u003csub\u003etotal\u003c/sub\u003e= F\u003csub\u003espring\u003c/sub\u003e*x\u003csub\u003e0\u003c/sub\u003e Eq.\u0026nbsp;(1)\u003c/p\u003e\u003cp\u003eThe support system is made of HEB-200 steel-arch profile and a 30 cm shotcrete layer. Prior to the collapse, an upgraded support system was adopted by doubling the HEB-200 profiles, and apply an additional 25 cm shotcrete layer.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe support maximum pressure and maximum deformation were calculated according to the Hoek \u0026amp; Brown (1980) [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] rock-support interaction approach.\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e sums up both HEB profiles and shotcrete characteristics.\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\u003eSupport characteristics\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\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eHEB-200 profiles\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eShotcrete\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eYoung modulus\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e210000 MPa\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e30000 MPa\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMoment of inertia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.00057 m\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.0036 m\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eResistance of the material\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e410 MPa\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e30 MPa\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSpacing\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.75 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\u003eThickness\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e/\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.3 m\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCross-section\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0781 m\u0026sup2;\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\u003ePoisson\u0026rsquo;s ration\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"3\"\u003eAccording to rock-support interaction method proposed by Hoek \u0026amp; Brown (1980), the pressure of the steel (Psmax) and shotcrete (Pcmax) elements give:\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd colspan=\"3\"\u003ePsmax\u0026thinsp;=\u0026thinsp;0.220105 MPa Pcmax\u0026thinsp;=\u0026thinsp;1.077115 MPa. The combined support pressure is made by the addition of both pressure, hence the maximum pressus (Pmax) gives us:\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ePcmax\u0026thinsp;=\u0026thinsp;Psmax\u0026thinsp;+\u0026thinsp;Pcmax\u0026thinsp;=\u0026thinsp;1.29722.\u003c/p\u003e\u003cp\u003eThe countermeasure support scheme first shotcrete layer is of 35 cm, and the second shotcrete layer is of 25 cm, so the updated support pressure (Pmax-2) gives us:\u003c/p\u003e\u003cp\u003ePmax-2\u0026thinsp;=\u0026thinsp;2.290787 MPa.\u003c/p\u003e\u003cp\u003eUmax-1 and Umax-2 are the maximum deformations of both support scheme calculated by the same method.\u003c/p\u003e\u003cp\u003eUmax-1\u0026thinsp;=\u0026thinsp;0.00366536 m, and Umax-2\u0026thinsp;=\u0026thinsp;0.003396509 m\u003c/p\u003e\u003cp\u003eThe Table \u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e recapitulates the total work of both support schemes according to Eq.\u0026nbsp;(1). The force is calculated by dividing the maximum pressure on the steel section, assuming of course that the force is applied perpendicularly to the same plane.\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\u003eProvided energy by the support systems\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"2\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSupport system\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eProvided energy (J)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eInitial support system\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e60541.8\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUpgraded support system\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e99624.57\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e3.1. Dynamic analysis\u003c/h2\u003e\u003cp\u003eBased on a 2D FEA model conducted using Abaqus with a dynamic/explicit solver to identify failure phenomena with a plastic behavior constitutive model, a nodal output is considered to effectively identify the inefficiency of the initially used support. The model geometry is 200 m long and 200 m deep, with a free mesh using a medial axis algorithm composed of 1,849 quadratic elements, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eTwo nodes were selected for output: the first at the crown of the tunnel in the immediate vicinity of the cavity, and a second at the upper vicinity of the excavation as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. The distance between both nodes is equal to that between two discretized elements, i.e., 2 m. The rock-burst phenomenon tends to accumulate energy, followed by a sudden release. Conversely, in ground with poor mechanical properties, the rock mass tends to loosen around the cavity. A perfect elasto-plastic model represents the behavior model in this case. An increase in plasticity can clearly reproduce the behavior in a plastic regime, with the loading accounted for by gravity loading. The parameters of the behavior are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab3\" 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\u003eBehaviour constitutive model used for the simulation\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\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=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eYoung modulus (MPa)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePoisson\u0026rsquo;s ratio\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eYield stress (KPa)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003ePlastic strain (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eUnit weight (KN/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e200\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e605\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e/\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e/\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e605\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e24\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e/\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e/\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e605\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e/\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e/\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e605\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e4.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\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\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e3.2. Feedback contribution\u003c/h2\u003e\u003cp\u003eIn Section 4 ( Results \u0026amp; Discussions ), it was found that the energy release exhibits substantial values. For this reason, a feedback contribution is proposed through a three-bench excavation method. This method is modeled using dynamic analysis with Abaqus FEA software, employing the same methodology mentioned earlier. A static analysis has also been carried out using PLAXIS V22 FEA software with the three-bench excavation method. From the proposed approach illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the energy output in PLAXIS is determined by the forces applied to the plate elements and the vertical phase displacements registered during the bench excavation.\u003c/p\u003e\u003cp\u003eThe Abaqus models in the feedback contribution share the same boundaries as the first model. The only difference is that the first model is created by excavating the crown first, while the second is modeled by excavating both the crown and the middle bench using the same meshing procedure, i.e., a free quadratic mesh with a medial axis algorithm, where the number of elements is 2028 and 1852, respectively, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e and \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eThe PLAXIS 2D model is 250 m long and 230 m deep, featuring a fine mesh with 962 elements and 7973 nodes, as indicated in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e. The loading is also considered as gravity, with the \"Hardening Soil Model \" adopted as the constitutive model. Tables\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e summarize the characteristics of the constitutive model and the lining material used for the simulation, respectively.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\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\u003eConstitutive model used in PLAXIS modelling\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"2\"\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\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eE50ref (MPa)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e400\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEoed ref (MPa)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e400\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEur ref (MPa)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e825\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eν ur\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePower \u0026ldquo;m\u0026rdquo;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.5\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePref (MN)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC (MN)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eΦ\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e24\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\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eLining material used for PLAXIS modelling\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\u003eProperties and units\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLining material\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eInvert material\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMaterial type\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eElastic\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eElastic\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLinear weight (KN/m/m)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e6.3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAxial stiffness (KN/m)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e8.33E6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.75E6\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBending stiffness (KN.m\u0026sup2;/m)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e92.38E3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e19.35E3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePoisson\u0026rsquo;s ratio\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Results and discussions","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e4.1. Dynamic analysis results\u003c/h2\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e and \u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e show the evolution of the energy release at the higher node (node 277, as indicated in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e) in both shear and compression components respectively S12 and S22.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSudden energy release is observed with magnitudes broadly superior compared to the energy of the initial support scheme. First, the original equilibrium is mainly in triaxial state, then disturbed with the presence of the cavity, which renders the problem in a bi-axial state. Failures are registered twice, in early and delayed failures, where both values of the early failure (i.e. 67576,43J) and delayed failure (-71610,41J \u0026amp; -69696,93J) are superior to the energy of the initial support system (see Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e, with compression component, the early failure (at 1\u0026amp; 2 with magnitudes reaching \u0026minus;\u0026thinsp;83291,7J \u0026amp; -83005,12 respectively) are still superior to the initial support system as well as with the delayed failure (-76056,43J). With the malfunction of the first support resulting in considerable deformations, the upgraded support system may not react properly or has a reduced margin than initially accounted for the presented situation.\u003c/p\u003e\u003cp\u003eThe Figs.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e and \u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e show the nodal output of the node 15 (see Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e.) in shear and compression components respectively.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe nodal output of the lower node in both shear and compression exhibits values significantly lower than the energy magnitude of the initial support scheme. In the direct contour of the excavation, the surrounding ground experiences a loosening pressure due to the energy release exerted initially.\u003c/p\u003e\u003cp\u003eThe recorded fluctuations in these curves are caused by iterative calculations and do not affect the analysis of the overall evolution law. Clearly, it can be observed that the SED of the surrounding rock at the tunnel wall shows a downward-upward-downward trend. When critical stress is reached, accumulated strain energy is released abruptly, leading to a drop in stored energy and stress, forming the \" saw tooth\" like curves. In the compression component (S22), the respective downward and upward movements are due to crack increase and crack closing (recovery and rise in crack closing), whereas in the shear component, the downward movement is due to crack increase and the upward trend results from crack closing with a positive value, which is synonymous with a tensile effect (lateral extent).\u003c/p\u003e\u003cp\u003eThis behavior is a result of an initial increase in strain energy as the load is applied to the cavity, followed by a sudden drop when a segment of crack jumps through a weak interface, then recovery and rise occur as cracks close or slow down in a harder portion. Near the excavation face, the three principal stresses of the rock mass decrease under the unloading effect of excavation, causing the decline and initial release of SED. In the tunnel section, the surrounding rock of the tunnel crown begins the stress redistribution evolution process under a biaxial stress state, and the stress continuously concentrates until reaching biaxial strength, leading to the accumulation and concentration of strain energy [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eIn previous research conducted by the authors [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], the left tunnel, prior to the collapse phenomenon, was undergoing a significant decompressed area extending up to a height of 40 m above the crown of the tunnel, established by numerical modeling with the relative shear stress component. The output was validated by the geophysical reconnaissance campaign, as demonstrated in the earlier research work.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e4.2. Feedback contribution with dynamic analysis\u003c/h2\u003e\u003cp\u003eAs suggested in the methodology section, considering the tunnel section as well, a feedback approach is proposed by changing the excavation technique given the amount of energy release recorded in section 4.1.\u003c/p\u003e\u003cp\u003eThe change in the excavation method has contributed to a decrease in the released energy, where the slower excavation pace registered the safest energy release in this case.\u003c/p\u003e\u003cp\u003eIn the part where the crown is excavated first, node 277 became node 21, and in the part where the crown and middle bench are excavated, the node designation will be node 187 (see Fig. 7). Figures\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003e and \u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003e show the energy evolution in the considered node with the shear and compression components, considering the crown excavation only.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eBoth Figs.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003e and \u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003e show a clear decrease in energy when the crown of the tunnel is excavated on its own; the peak energy releases are recorded at 50,148 J in compression and 52,480 J, which is a lower value compared to the initial support scheme (see Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The displacements should normally decrease with the reduction of the excavated section, leading to a more gradual release of strain energy, which provides a sufficient margin for reaction during the excavation process compared to a larger section, considering the poor mechanical properties of the surrounding rock where the tunnel is excavated.\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e18\u003c/span\u003e and \u003cspan refid=\"Fig19\" class=\"InternalRef\"\u003e19\u003c/span\u003e show the energy evolution in the considered node, including the shear and compression components, when both the crown and the middle bench are excavated.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIn a more critical section, the stress redistribution is higher, resulting in a greater energy release during excavation. In this case, peaks are recorded at 80015.3 J and 69318.37 J in the compression and shear components, respectively. These values exceed the provided energy of the initial support scheme but remain below the maximum provided energy from the upgraded support system. However, in the compression component, the exhibited value has a closely critical safety margin (with a margin of 19.67%). During the construction phase, the surrounding ground experiences time -dependent degradation, as the tunneling process has an evident temporal-dimensional effect [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e4.3. Feedback contribution with static analysis\u003c/h2\u003e\u003cp\u003eThe static analysis has been carried out using PLAXIS V22 with 2D plane strain analysis. The modeling methodology is described in Section 3.2, the input data are detailed in Tables\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, and the mesh is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eFigures \u003cspan refid=\"Fig20\" class=\"InternalRef\"\u003e20\u003c/span\u003e and \u003cspan refid=\"Fig21\" class=\"InternalRef\"\u003e21\u003c/span\u003e respectively show the vertical phase displacements and the applied axial force for the crown and middle bench excavation methods.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eWith the recorded 0.046 m vertical displacements and the applied axial forces on the plates of 1392 KN, the calculated energy should then be 64032 J by this proposed method.\u003c/p\u003e\u003cp\u003eThe Figs.\u0026nbsp;\u003cspan refid=\"Fig22\" class=\"InternalRef\"\u003e22\u003c/span\u003e and \u003cspan refid=\"Fig23\" class=\"InternalRef\"\u003e23\u003c/span\u003e respectively show the vertical phase displacements and the applied axial force respectively for the crown excavation only.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eWith the recorded 0.07 m vertical displacements and the applied axial forces on the plates of 1358 KN, the calculated energy should then be 93702 J by this proposed method.\u003c/p\u003e\u003cp\u003eThe results output can seem a bit confusing since the lower excavation section exhibits higher energy in the output; however, in the stability analysis, during the excavation of the crown, there is a deadweight that has been released at the level of the roof, making the crown of the tunnel more prone to instabilities during tunneling, especially if this part of the tunnel is excavated first. When the excavation of the crown and the middle bench is carried out, the stress redistribution is also applied to the sidewalls of the tunnel, which somewhat alleviates the additional stress endured on the roof. Other excavation methods can also be proposed to mitigate the risks related to tunnel excavation.\u003c/p\u003e\u003c/div\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eIn this study, an investigation of the strain energy evolution has been carried out using numerical simulations in both dynamic and static cases prior to a ground collapse in a large section soft rock tunnel due to insufficient support performance.\u003c/p\u003e\u003cp\u003eThrough finite element analysis (FEA) dynamic analysis, it was demonstrated that the initial support could no longer withstand the surrounding rock reaction due to the excavation process, as indicated by nodal output at the crown of the tunnel in compression and shear components, where the support failed to provide sufficient energy to counteract the ground reaction. Moreover, the countermeasure support exhibited adequate energy compared to the ground reaction, but not with a broad safety margin, which may compromise the integrity of the infrastructure in the long term.\u003c/p\u003e\u003cp\u003eAt a certain point, changing and/or upgrading the support system does not necessarily yield the expected performance; the ground reaction must be anticipated according to the stress release rather than the applied support capacity, so as to increase the rock mass bearing capacity. For practical purposes, altering the excavation process is the best solution to adopt, given that the surrounding ground will react excessively and that the support, even if it provides sufficient pressure, may undergo time-dependent deformation that could affect its performance.\u003c/p\u003e\u003cp\u003eIn the static analysis, a typical solution for stability analysis is provided, where the plate elements undergo energy release. From this perspective, the analysis showed a limit equilibrium where the energy release was less than the energy provided by the countermeasure support but with a low safety margin, which may lead to a critical situation during the tunneling process. By altering the excavation process, the released energy decreased due to the reduction in section size but remained significant at the crown of the tunnel due to the deadweight effect on the tunnel roof.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgment\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAuthors express their deep gratitude for granting access to the construction yard, as well as their accompanying during the internship of the first author. Authors are also thankful to the responsible society of the constructions for their help and providing the necessary data for this work’s fulfilment.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors’ contribution\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cu\u003eAllouache Abdelaziz N\u003c/u\u003e: Conceptualization, Data acquisition, Investigation, Data curation, Formal analysis, Methodology, Plaxis Software, Supervision, Validation, Original draft.\u003c/p\u003e\n\u003cp\u003e\u003cu\u003eBensehamdi Salim\u003c/u\u003e: Data curation, Formal analysis, Investigation, Project administration, Supervision, Visualisation, review \u0026amp; editing.\u003c/p\u003e\n\u003cp\u003e\u003cu\u003eNettour Djamel\u003c/u\u003e: Supervision, Visualization, Review \u0026amp; editing.\u003c/p\u003e\n\u003cp\u003e\u003cu\u003eSaurabh Kureel\u003c/u\u003e: Abaqus software, Supervision, Review \u0026amp; editing.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work did not receive any funding, or any specific grant from any part of any kind.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAuthors of this work declare that there are no competing interests, conflicts, or any related conflicts of interests from any part of any kind\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAI use declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors used AI assistance for a grammar check purpose (link: https://www.zerogpt.com/)\u003c/p\u003e\n\u003cp\u003eDuring the preparation of this work the authors used “Zero GPT” AI tool (link: https://www.zerogpt.com) in order to check the grammar and spelling. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eLi G, Luo Z, Wu C, Lu H (2024) C. Zhu Integrated early warning and reinforcement support system for soft rock tunnels: a novel approach utilizing catastrophe theory and energy transfer laws Tunn Undergr Space Technol, 150 Article 105869. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.tust.2024.105869\u003c/span\u003e\u003cspan address=\"10.1016/j.tust.2024.105869\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eCai WQ, Zhu HH, Liang WH (2022a) Three-dimensional tunnel face extrusion and reinforcement effects of underground excavations in deep rock masses. Int J Rock Mech Min Sci 150:104999\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eCai WQ, Zhu HH, Liang WH (2022b) Three-dimensional stress rotation and control mechanism of deep tunneling incorporating generalized ZhangeZhu strength-based forward analysis. Eng Geol 308:106806\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLi G, Ma F, Guo J, Zhao H (2021b) Case study of roadway deformation failure mechanisms: Field investigation and numerical simulation. Energies 14:1032\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLi J, Hu M, Ding E, Kong W, Pan D, Chen S (2016) Multi-parameter numerical simulation of dynamic monitoring of rock deformation in deep mining. Int J Min Sci Technol 26:851\u0026ndash;855\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSakcali A, Yavuz H (2019) Estimation of radial deformations around circular tunnels in weak rock masses through numerical modelling. Int J Rock Mech Min Sci 123:104092\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSong Z, Yang T, Jiang A, Zhang D, Jiang Z (2016) Experimental investigation and numerical simulation of surrounding rock creep for deep mining tunnels. J South Afr Inst Min Metall 116:1181\u0026ndash;1188\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBai C, Xue Y, Qiu D, Su M, Ma X, Liu H (2021) Analysis of factors affecting the deformation of soft rock tunnels by data envelopment analysis and a risk assessment model. Tunn Undergr Space Technol 116:104111\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLiu W, Chen J, Chen L, Luo Y, Shi Z, Wu Y (2022) Nonlinear deformation behaviors and a new approach for the classifcation and prediction of large deformation in tunnel construction stage: a case study. Eur J Environ Civ Eng 26:2008\u0026ndash;2036\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eXue Y, Zhang X, Li S, Qiu D, Su M, Li L, Li Z, Tao Y (2018) Analysis of factors influencing tunnel deformation in loess deposits by data mining: a deformation prediction model. Eng Geol 232:94\u0026ndash;103\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eParsapour D, Fahimifar A (2016) Semi-analytical solution for time-dependent deformations in swelling rocks around circular tunnels. Geosci J 20:517\u0026ndash;528\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eXiaolin C, Weiming G, Fengxi Z, Guoliang D (2019) Stress analytical solution for shallow buried lined circular tunnel under the deformation of surrounding rock inner edge. Geotech Geol Eng 37:3771\u0026ndash;3780\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYang Z, Xu J, Feng Q, Liu W, He P, Fu S (2022) Elastoplastic analytical solution for the stress and deformation of the surrounding rock in cold region tunnels considering the influence of the temperature feld. Int J Geomech 22:04022118\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZareifard MR, Fahimifar A (2016) Analytical solutions for the stresses and deformations of deep tunnels in an elastic-brittle-plastic rock mass considering the damaged zone. Tunn Undergr Space Technol 58:186\u0026ndash;196\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSun C, Chen DX, Wang LG et al (2021) Quantitative evaluation of the constraint effect and stability of tunnel lining support. Tunn Undergr Space Technol 112:103920\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLeone T, Nordas AN, Anagnostou G (2023) Effects of Creep on Shield Tunnelling Through Squeezing Ground. Rock Mech Rock Eng\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eXu GW, Gutierrez M, Arora K et al (2022) Visco-plastic response of deep tunnels based on a fractional damage creep constitutive model. Acta Geotech 17:613\u0026ndash;633\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhang JB, Du RH, Zhang XH et al (2023) Experimental and numerical investigation of the rheological characteristics of tunnels in cold regions during excavation and operation. Acta Geotech\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eALLOUACHE AN, Bensehamdi S, Hrubesova E et al (2025) Geomechanical Back Assessment of a Major Ground Collapse of a Twin Tunnel located in the Eastern Section of the Algerian Highway. Indian Geotech J. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s40098-025-01177-8\u003c/span\u003e\u003cspan address=\"10.1007/s40098-025-01177-8\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHoek E, Brown ET (1980) Underground Excavations in Rock. London. Institution of Mining Metallurgy. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1201/9781482288926\u003c/span\u003e\u003cspan address=\"10.1201/9781482288926\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLiu Y, Zhang R, Hou S et al (2025) Investigation of energy evolution process of rock mass during deep tunnel excavation based on elasto-viscoplastic damage model and time-dependent energy indices. Acta Geotech 20:1549\u0026ndash;1570. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s11440-024-02485-8\u003c/span\u003e\u003cspan address=\"10.1007/s11440-024-02485-8\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAydan O\u0026uml;, Akagi T, Kawamoto T (1993) The squeezing potential of rocks around tunnels: theory and prediction. Rock Mech Rock Eng 26:137\u0026ndash;163\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSingh M, Singh B, Choudhari J (2007) Critical strain and squeezing of rock mass in tunnels. Tunn Undergr Space Technol 22(3):343\u0026ndash;350\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Energy release, ground collapse, dynamic analysis, soft rock tunnel, FEA simulation","lastPublishedDoi":"10.21203/rs.3.rs-7312555/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7312555/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this study, the surrounding ground mass energy release was investigated to demonstrate the inefficiency of the support system prior to a major ground collapse in a twin freeway tunnel excavated in a soft surrounding rock mass (with poor mechanical properties) using simulation. Unlike hard rocks, soft rocks tend to soften in the immediate vicinity of the underground excavation, as demonstrated in this case by a nodal output. Through dynamic analysis, it has been proven that the ground energy release has exceeded the energy provided by the support system, and the countermeasure support has a limited safety margin despite supplying sufficient energy. A feedback approach is proposed through a change in the excavation method, which has proven to be an efficient way to reduce ground energy release during the tunnel excavation process.\u003c/p\u003e","manuscriptTitle":"Investigation on the strain energy release prior to a major ground collapse of a large section soft rock tunnel","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-08 16:35:25","doi":"10.21203/rs.3.rs-7312555/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":"bdee882b-1bee-4f66-9078-1a38b158c40c","owner":[],"postedDate":"August 8th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":52769967,"name":"Civil Engineering"},{"id":52769968,"name":"Geology"}],"tags":[],"updatedAt":"2025-08-08T16:35:25+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-08 16:35:25","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7312555","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7312555","identity":"rs-7312555","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}