Stress-deformation and stability challenges in Himalayan tunnels: impact of geological discontinuities

Abstract

This study investigates stress-deformation behavior in Himalayan tunnels, focusing on how geological features impact stability. The objective is to enhance the understanding of displacement phenomena, particularly in tunnels traversing jointed rocks. A modified support system, to specific rock mass classifications, is employed to address the unique challenges posed by geological discontinuities. Kinematic analysis reveals a 20% probability of wedge failure due to these discontinuities. Numerical analysis using Hoek–Brown parameters identifies significant stress concentrations at the tunnel crown, especially in jointed sections, where increased convergence and displacement (1.2 mm at the crown compared to 0.25 mm at the walls) highlight the susceptibility to deformation. The study indicates the critical need for specialized support in jointed regions to mitigate stability risks.

Article highlights

This study contributes understanding of complex interactions between geological features and tunnel stability, regarding stress-deformation phenomena in Himalayan tunnels.

The analysis identifies significant stability concerns, including a concerning 20% probability of wedge failure and increasing stress levels at the tunnel crown. It underscores the importance of support systems and proactive risk management strategies to mitigate instability risks, particularly in ultramafic sections characterized by higher stresses.

The research highlights the importance of considering dynamic loading conditions, validation with field data, and long-term variations in stress and deformation for a comprehensive understanding of tunnel stability. Future investigations should explore the influence of groundwater flow and seismic information, to examining advanced support systems.

Introduction

In the realm of modern infrastructure development, tunnels play a key role, serving as vital channels for transportation, utilities, and various other applications. Ensuring the successful construction and operation of tunnels is dominant to maintaining the efficiency and safety of these essential passageways. However, challenges arise when tunnels intersect with the intricate geological characteristics of the surrounding rock mass, particularly in proximity to caves or voids. The stability and performance of tunnels can be significantly affected by factors such as cavity size, necessitating a comprehensive understanding of their dynamic behaviour. Key factors influencing tunnel stability include displacement, shear force, bending moment, and axial force. Investigating the interaction of these factors is critical for enhancing understanding of tunnel behaviour and advancing the reliability and sustainability of tunnel infrastructure amidst geological complexities.

Precise and dependable forecasts of rock deformations are crucial in a myriad of projects across civil and mining engineering that entail working with rock materials. Assuring the precision of these predictions is paramount for optimizing the design and safety of structures and the efficient planning and execution of mining operations [1]. Initially the tunnel stability analysis was performed by empirical methods [2] and rock mass classifications [3], however the movement in rock mass around the tunnel crown and wall is determined by numerical modelling [4]. The deformation and failure processes occurring during tunnel excavation are fundamental concerns in geotechnical projects [5–7]. The rock mass classifications include the rock mass rating and Tunnelling Quality index [8], which have some successful reports along the Himalayas as well [9, 10]. Zia reported that while empirical methods can produce satisfactory underground structures, they do not sufficiently evaluate the excavation's response or the effectiveness of the installed support systems [11]. Dealing with rock mass’s non-elastic, non-linear, and anisotropic behaviour poses significant challenges for empirical methods [12]. Since the rock mass strength is rock-dependent and is influenced by exposure to extreme temperature variations and loading conditions empirical design methods do not provide sufficient information. The numerical modelling incorporate the ground conditions and they are dependent on tunnel shape and size [13] sometime this makes the modelling more complex [14]. Given the flexibility of input parameters and the availability of detailed ground information such as stresses and ground displacement, preference is often given to numerical modelling over empirical methods [15]. The stress field and displacement field derived from numerical results can aid in interpreting the mechanism of tunnel failure [16]. When employing analytical methods to determine the shallowest overburden thickness, prioritizing the consideration of shear force based on a nonlinear soil resistance model is advantageous for ensuring the anti-floating stability of shield tunnels without necessitating excessive anti-floating capacity [17]. Abbas et al. modified the RMR and Q systems for tunnelling in the Himalayas, and the recommended support systems were adapted based on these modified RMR and Q classifications [10]. Rehman et al. studied the uses and limitations of these empirical systems for tunnel design. Their results indicate that incorporating ground behavior into the analysis makes the application of these empirical systems more beneficial for the preliminary design of tunnels [18]. Shahriar et al. recently conducted a comparison of rock mass classification systems for tunneling and found that joint set orientation and joint set number are critical parameters contributing to weak correlation coefficients [19]. However, numerical modelling for tunnelling along Himalayas has not verified the empirically suggested support.

In tunnel engineering, the initial in-situ stress state undergoes disruption, leading to the redistribution of stress after tunneling [20]. Numerous challenges can emerge when encountering high in-situ stress conditions, including elevated stress levels, intense unloading, high seismic activity, and other complex geological environments. These challenges encompass extensive relaxation depths, significant displacements, occurrences of collapse, and rock bursts [21]. During tunnel construction, monitoring the necessary tunnel face support pressure is a critical parameter affected by the presence of water inflow [22], this may decrease the stability of the tunnel [23]. Analytical solutions, including applying the limit equilibrium method, have been developed to study the stability of tunnel faces. These solutions have been successfully applied in various tunneling projects [24]. Yet, employing a Limit Analysis upper bound solution to calculate the stability of a tunnel face, while considering the influence of advance drainage, has not been previously utilized [25].

The FLAC3D numerical modeling technique is utilized to investigate the distribution characteristics of stress fields, strain fields, and plastic zones within the surrounding rock mass of underground excavations, including mining and tunneling projects [26]. Underground structures, notably tunnels, frequently intersect with faults, rendering them susceptible to fault movement. Before evaluating stability using FLAC3D numerical modelling, it is imperative to possess a thorough understanding of the actual ground conditions. Therefore, during site investigations for underground structure construction, significant emphasis should be placed on identifying and comprehending the presence of faults. This enables informed decision-making and the implementation of effective mitigation measures [26]. Measuring the displacement of tunnel walls and crown presents a significant challenge. Studies have shown that the rapid redistribution of in-situ stress resulting from the swift unloading of tunnel excavation is a major contributing factor to tunnel failures. This underscores the importance of comprehending and effectively managing the disturbance in the surrounding rock during tunnel construction [27]. As the level of in-situ stress rises, the damage induced by the instantaneous redistribution effect of stress may exceed that caused by explosions, emerging as the primary factor contributing to structural damage [28]. In conditions of high in-situ stress, instant excavation disrupts the surrounding rock, revealing various internal mechanisms at different scales [29, 30]. To evaluate the effectiveness of 2D deconfinement methods, numerical investigations are conducted. These methods entail integrating pre-displacements of the soil surrounding the tunnel before installing the tunnel structure, aiming to simulate the three-dimensional phenomenon occurring at the tunnel face [2, 31]. With an increasing distance below the tunnel span, the displacement of the tunnel ceiling tends to rise. Furthermore, the bending moment generally increases while the axial force tends to decrease, although these changes are contingent upon the size of the cave [32]. The literature has also reported the application of analytical methods [33] machine learning and finite element method in the installation of reinforcement to New Austian tunnelling method [34]. The application of a Neuro-fuzzy inference system for estimating the field penetration index of a tunnel boring machine in rock mass has also been studied. This approach enhances the accuracy of predictions and contributes to the optimization of tunnelling processes [35]. However, the application of numerical modelling in jointed rock mass for tunnelling along the Himalayas has received limited attention.

The primary objective of this study is to enhance the understanding of stress-deformation behaviour in Himalayan tunnels, with a particular focus on the influence of geological features on tunnel stability. This research is original in its approach, as it specifically investigates the unique challenges posed by ultramafic rocks and their associated geological discontinuities. By employing a modified support system based on rock mass classifications, this study aims to address the limitations of existing empirical methods and improve the effectiveness of tunnel design in these complex geological settings. The findings of this study are expected to provide valuable results for optimizing support systems in regions with similar geological characteristics, ultimately contributing to safer and more reliable underground construction practices.

In the following section, the research methodology and regional geology are discussed. Discontinuities within the geological formations were carefully examined to understand their implications. Detailed chemical analyses of gabbronorite (rock type I) and ultramafic (rock type II) were conducted to explain their compositions and properties. The results were thoroughly discussed, leading to valuable conclusions regarding the studied geological characteristics. The methodology, discontinuity analysis, and regional geology have been discussed in Sect. 2. The results related to displacement and stress scenarios in tunnel crown and walls have been discussed in Sect. 3. Finally, the conclusions and recommendations are given in Sect. 4.

Methodology and the geological setting

Tunnelling through the Himalayas presents difficult challenges owing to the historical tectonic activities that have disrupted the rock mass [36]. The study area stands as a geological wonder renowned for its diverse array of rock formations, particularly characterized by rock type-I and rock type II. Rock type-I, a coarse-grained igneous rock abundant in plagioclase feldspar and pyroxene minerals, dominates significant stretches, formed through the gradual cooling and crystallization of deep-seated magma within the Earth's crust. The ultramafic rocks, distinguished by their high concentrations of magnesium and iron-bearing minerals such as olivine and pyroxene, add to the geological tapestry [11].

The geological composition, particularly in terms of chemical content, significantly influences the choice of support criteria and rock mass stability during tunnel construction. The composition of mineral contents in two prevalent types of rock mass along the tunnel route, namely rock type-I and rock type-II [37] is depicted in Fig. 1. Analysis reveals that rock type-I exhibits a higher percentage of SiO₂, while rock type-II demonstrates higher levels of MgO. This difference emphasizes the requirement for suitable support strategies and particular considerations to navigate the distinct geological challenges posed by these rock types during tunnelling operations in the Himalayan region.

Fig.1 [Images not available. See PDF.]

Chemical composition of rock types along tunnel route

In this manuscript, kinematic analysis was performed to determine potential failure modes along the tunnel route, using input parameters from the Hoek–Brown criteria for numerical modeling conducted with FLAC 3D. For support design, the empirical approach suggested by Bieniawski's modified support system was utilized, as detailed in the below section. In addition to empirical and theoretical methodologies, the assessment of tunnel performance has integrated statistical-based models, encompassing both multiple and simple regression techniques. These models helps the understanding of factors that influence tunnel behaviour [38].

The Mohr–Coulomb criteria, commonly used for characterizing rock failure, have a tendency to overestimate the tensile strength and lack a maximum limit on shear strength tolerance for rocks [39]. This limitation underscores the importance of considering alternative criteria and refining the assessment of rock failure mechanisms. Moreover, the absence of a maximum limit on shear strength tolerance in the Mohr–Coulomb criteria raises concerns about potential underestimation of the rocks' resistance to shear forces, emphasizing the need for a comprehensive evaluation incorporating additional failure criteria in geotechnical analysis. This research utilized the original Hoek–Brown Criterion, deemed more suitable for numerical modelling [40]. The Hoek–Brown criterion, applicable not only to rock materials but also to rock masses, is expressed as follows:

1

$$\frac{{\sigma }_1}{{\sigma }_{\mathit{ci}}}=\frac{{\sigma }_3}{{\sigma }_{\mathit{ci}}}+{\left(m,b,\frac{{\sigma }_3}{{\sigma }_1},+,s\right)}^a$$

The equation above is the generalized Hoek–Brown criterion of rock mass. The Hoek–Brown criterion for intact rock material is a special form of the generalized equation when s = 1 and a = 0.5. For intact rock, mb becomes mi, i.e.

2

$$\frac{{\sigma }_1}{{\sigma }_{\mathit{ci}}}=\frac{{\sigma }_3}{{\sigma }_{\mathit{ci}}}+{\left(m,i,\frac{{\sigma }_3}{\sigma 1},+,s\right)}^{0.5}$$

In the Hoek–Brown criterion, the symbol σ_ci consistently represents the uniaxial compressive strength of intact rock material. The parameters s, a, mi, and mb are essential input parameters needed for FLAC3D to analyse the stress and displacement around the tunnel. One of the most crucial parameters to consider when designing tunnel excavations is the uniaxial compressive strength [41]. This applies both to the Hoek–Brown criterion for individual rock material and for rock masses. In the broader context of the generalized Hoek–Brown criterion, σ₁ signifies the strength of the rock mass under a confining pressure σ₃.

Parameter “a” is typically set at a value of 0.5. The constants “mb” and “s” are parameters that vary with the type of rock and the quality of the rock mass. The specific values of “mb” and “s” recommended by Hoek for various rock types can be found in Table 1.

Table 1. Relation between rock mass quality and Hoek–Brown constants [42]

Hoek–Brown failure criterion	s	Carbonates	Lithified argillaceous	Arenaceous	Fine-grained polyminerallic igneous	Coarse-grained polyminerallic igneous and metamorphic
Intact rock material	1	7	10	15	17.0	25.0
Very good rock	0.1	3.5	5	7.5	8.5	12.5
Good rock mass	0.004	0.7	1	1.5	1.7	2.5
Fair rock mass	0.0001	0.14	0.20	0.30	0.34	0.50
Poor rock mass	0.00001	0.04	0.05	0.08	0.09	0.13
Very rock mass	0	0.007	0.01	0.015	0.017	0.025

There is an alternate way to find the parameters “a”, “mb” and “s” using Geological Strength Index (GSI) as given below.

3

$$mb=mi\text{exp}\left(\frac{GSI-100}{28}\right)$$

For GSI > 25, which corresponds to rock masses of good to reasonable quality, the original Hoek–Brown criterion is applicable with its parameters set as follows:

4

$$s=mi\text{exp}\left(\frac{GSI-100}{9}\right)$$

And a = 0.5

indicating rock masses of very poor quality, s = 0, and the value of “a” in the Hoek–Brown criterion is no longer equal to 0.5. The value of a can be estimated from GSI by the following Eq. (5).

5

$$a=0.65-\frac{\mathit{GSI}}{200}$$

A three-dimensional numerical model of the tunnel was developed using FLAC3D 6.0 software [32]. The model geometry and dimensions were based on the actual tunnel design, incorporating the surrounding rock mass, support systems, and excavation sequence. The schematic diagram of the methodology is presented in Fig. 2. The rock mass was characterized using appropriate constitutive models based on geotechnical properties obtained from laboratory tests. These material models accounted for factors such as nonlinear behaviour, strength anisotropy, and time-dependent effects. Boundary conditions were applied to simulate the loading and excavation process, encompassing initial stress conditions, external loads, and support system installation. The support system was modelled using appropriate boundary conditions, such as fixed or prescribed displacements.

Fig. 2 [Images not available. See PDF.]

The schematic diagram depicts the research methodology

FLAC3D software was employed to simulate the excavation and loading stages, taking progressive deformation and stress redistribution while considering time-dependent effects and non-linear behaviour of the rock mass. The obtained results were analysed to evaluate stress distribution, convergence behaviour, and displacement magnitudes at the tunnel crown and walls. Post-processing techniques, including contour plots, displacement profiles, and stress distribution graphs, were utilized to visualize and interpret simulation results Fig. 3.

Fig. 3 [Images not available. See PDF.]

The kinematic analysis of discontinuities sets

The numerical model underwent validation by comparing simulated results with available field measurements, such as convergence monitoring data, displacement surveys, and stress measurements. This validation process aimed to assess the accuracy and reliability of the numerical model in reproducing observed behaviour.

The kinematic analysis has been performed using the discontinuity parameters from Table 2. These parameters likely include information about the orientation, spacing, persistence, roughness, and other characteristics of the discontinuities present in the rock mass. These parameters play a critical role in assessing the potential failure modes and stability of the tunnel [17].

Table 2. Discontinuity conditions in a single round along the tunnel route

Discontinuity Type	Dip	Dip direction	Roughness	Aperture	Infilling	Persistence	Spacing	Weathering
J1	20°	300°	Very rough	Partial opening	Calcite	10–20	Moderate	Slightly wet
J2	55°	65°	Slightly rough	Tight	Calcite	3–10	Wide	Slightly wet
J3	83°	190°	Slightly rough	Partial opening	Calcite	3–10	Moderate	Slightly wet
J4	65°	210°	Very rough	Tight	Calcite	3–10	Wide	Slightly wet
J5	70°	220°	Very rough	Tight	Calcite	3–10	Wide	Slightly wet

Each round of tunnel excavation advances up to 3 m and it was observed that most of the advances have discontinuity number up to 6. The presence of up to 6 joints within each round of excavation highlights the potential for multiple discontinuities to interact and influence the stability of the tunnel. The orientations and interactions of these joints can significantly affect the behaviour of the rock mass and the potential for failure. In case of water conditions, most of the tunnel route was dry to wet. The variation in water conditions along the tunnel route, from dry to wet or flowing, adds an additional layer of complexity to the stability assessment. The RMR system, provide a systematic way to quantify the engineering properties of a rock mass and assess its stability. The fact that wet conditions are evaluated according to these criteria indicates a comprehensive approach to understanding the effects of water on the tunnel’s stability after incorporating all the parameters the empirical support is suggested and its validity is assessed by numerical modeling in the below section.

Kinematic analysis, using discontinuity data (Table 2), shows no likelihood of planar failure (0%, Fig. 4) or toppling (0%, Fig. 6), indicating good structural stability against these modes. The absence of planar and toppling failures suggests that the tunnel zone’s discontinuity orientations and strengths do not favor these types of failures. However, there is a 20% chance of wedge failure Fig. 5, indicating a higher likelihood compared to other failure modes. Wedge failures, involving sliding or toppling within a wedge-shaped space between discontinuities, suggest that certain discontinuity orientations could lead to instability. Although 20% is not excessively high, it warrants careful monitoring and mitigation. Contributing factors include variations in rock mass strength, presence of potential sliding surfaces, groundwater pressure, seismic activity, and stress concentrations at structural irregularities Fig. 6.

Fig.4 [Images not available. See PDF.]

The percentage of planer failure using kinematic analysis

Fig. 5 [Images not available. See PDF.]

Analysis of potential failure of wedge using kinematic analysis

Fig. 6 [Images not available. See PDF.]

Analysis of potential toppling failure using kinematic method

The study area is primarily characterized by the Kohistan Island Arc (KIA), which is delineated by two distinct suture zones: the Main Karakoram Thrust (MKT) or Shayok Suture Zone to the north, and the Indus-suture or Main Mantle Thrust (MMT) to the south [43]. The geological map of the study area is provided in Fig. 7. These formations demarcate the KIA from much larger and older geological entities in the surrounding region. Extending approximately 700 km, the KIA spans westward into Afghanistan and eastward into the Indian region of Ladakh, presenting the most complete representation of the Kohistan-Ladakh terrane in terms of exposed geological units. Afghanistan’s region is relatively small, while Ladakh mainly comprises upper crustal units [44]. The study site falls within the Chilas Mafic Igneous Complex Fig. 7, distinct from an ophiolite formation. Extending to a depth of 40 km and stretching for 300 km, the Chilas mafic complex comprises plagioclase, orthopyroxene, clinopyroxene, ilmenite, magnetite, quartz, hornblende, scapolite, and biotite. The rocks within this complex exhibit a petrographic nature resembling plutonic blocks [26]. The tunnel route traverses through sections of rock type-I and rock type-II.

Fig. 7 [Images not available. See PDF.]

Geologic map of northern Pakistan showing the Kohistan arc terrane [45], the area studies here is near Chilas Stratiform complex

Results and discussion

The stress distribution, deformation patterns, and displacement magnitudes at the tunnel crown and walls have been investigated using FLAC3D software for rock type-1 and rock type 2 in the given section. The properties of rock types are given in Table 3.

Table 3. Properties of rock types

Rock type	UCS (MPa)	Modulus of elasticity (GPa)	Poisson ratio	mb	s	a	Tensile strength (MPa)
Type-1	80	40	0.25	8	0.051	0.5	8
Type-2	50	30	0.26	1.2	0.00058	0.5	5

The analysis of stresses and displacement along rock type-I

The displacement magnitude at the tunnel crown (Fig. 8) is higher for rock type-I, indicating greater deformation compared to the side walls. This suggests higher stress concentrations or weaker rock conditions at the crown. Installing U-shaped steel components and new confined concrete arches can effectively control this displacement [46]. Anchor cables commonly face challenges in adequately absorbing the energy released from rock deformation due to their limited elongation and low safety margin. This often leads to failures in supporting structures [47]. Displacement magnitudes in the rock mass stress field range from 0.009 mm to 7 mm, reflecting variations in deformation. The 7 mm displacement indicates higher stress concentrations or weaker rock, while the 0.009 mm suggests lower stress or more competent rock. Increased displacement at the tunnel crown may result from overburden pressure, ground movement, or geological structures. Numerical modeling is effective for assessing ground displacement [48]. Accurate estimation of potential ground movement due to tunnelling is fundamental for safety evaluation of adjacent facilities [2]. Figure 8 shows the magnitude of displacement across the tunnel.

Fig. 8 [Images not available. See PDF.]

The displacement magnitude across rock type-I

Displacement magnitudes along the Z direction Fig. 8 show that the tunnel crown experiences a slightly higher displacement of 1.2 mm compared to 0.25 mm along the walls. This suggests the crown is more prone to deformation, potentially due to stress concentrations, geological conditions, or variations in rock mass properties. In Zone X Fig. 8, displacement is uniform at 0.1 mm along both the tunnel crown and side walls, indicating consistent deformation and similar stress conditions in this zone. This uniform displacement suggests balanced stress distribution and effective load transfer within Zone X. Comparing the uniform displacement in Zone X to the higher displacement along the Z direction highlights differences in deformation behavior and stress distribution. Additionally, the minimum principal stress (σ₃) values in the rock mass range from − 0.5 MPa to − 6 MPa, indicating a range of tensile stresses.

Intermediate principal effective stress values range from − 0.2 MPa to − 2.4 MPa, affecting shear strength and failure mechanisms. Maximum principal stress (σ₁) ranges from − 0.05 MPa to − 0.8 MPa, indicating compressive stresses. These stress values are essential for assessing stability and determining support needs. Volumetric effective stress is higher at the crown than at the walls, indicating stress distribution variations Fig. 9. Convergence is greater at the walls and invert than at the crown Fig. 10, suggesting increased deformation and closure at these areas.

Fig. 9 [Images not available. See PDF.]

The scenario of stresses along the portion of rock type-I

Fig. 10 [Images not available. See PDF.]

Estimation of tunnel Convergence factor

The stress-to-strength ratio Fig. 11 and Fig. 15 is a measure of the relative stress level compared to the strength of the material. The stress-to-strength ratio provides an indication of the safety margin or factor of safety in the rock mass. The stress-to-strength ratio can also be used to evaluate the risk of potential failure in the rock mass. If the ratio is relatively low, indicating a significant safety margin, the risk of failure is lower. Conversely, a higher ratio suggests a higher risk of failure since the stress levels are closer to the strength [30]. Commonly encountered in tunnels, weak zones often involve active swelling loose infilling, constituting a prevalent phenomenon. The presence of water seepage within these zones can substantially decrease standup time and escalate excavation challenges [26].

Fig. 11 [Images not available. See PDF.]

Stress-strength ratio across the tunnel route

Most of the rocks in the region exhibit a brittle nature, as indicated by the high silica content depicted in Fig. 1. Evaluating rock brittleness is a critical parameter in any ground excavation effort, playing an essential role in the design of geotechnical engineering structures, particularly those constructed on rock masses [49]. Proper consideration of rock brittleness is essential for ensuring the resilience and stability of such structures, making it imperative to incorporate this key property in geotechnical engineering projects. The presence of rocks within fault zones has the potential to redirect groundwater toward the tunnel, creating challenging conditions in that section. Additionally, certain segments of the tunnel path, particularly the central area characterized by strong layer folding, exhibit concentrated fractures and discontinuity systems influencing the rock masses. These areas, referred to as fracture zones, consist of rugged and weathered rock in a significantly compromised fracture state filled with clay and calcite under high in-situ stress conditions. This condition is identified as the primary cause of instability along the Lalehzar fault [26].

The analysis of stresses and displacement along rock type-II

The stress analysis using numerical modeling, as shown in Fig. 12, indicates that the ultramafic section is more vulnerable and requires additional support for tunnel stability compared to the rock type-I sections. Higher shear stress values observed above the crown and side walls near excavations confirm this instability. The increased vulnerability in the ultramafic section may result from its high strength but low ductility, which can lead to sudden failure under stress. Additionally, geological discontinuities or fault zones within the ultramafic rock mass could intensify stress concentrations and further compromise stability [50]. Moreover, the differences in mechanical properties between ultramafic and rock type-I, such as elastic modulus and Poisson’s ratio, contribute to variations in stress distribution and deformation behavior, as these are key input parameters in FLAC 3D modeling. The heterogeneous nature of ultramafic formations may also create irregularities in the rock mass, leading to localized stress concentrations and potential instability zones [51]. Given these observations, it becomes important to implement appropriate support measures, such as reinforced shotcrete, rock bolts, or ground reinforcement techniques, to enhance the stability and safety of the tunnel in the ultramafic section as suggested by Bieniawski[52]. Moreover, continuous monitoring and analysis of stress distribution along the tunnel alignment are critical for proactive risk management and timely intervention to mitigate potential stability issue [53].

Fig.12 [Images not available. See PDF.]

The stresses along rock type-II of tunnel route

Figure 13 illustrates displacement in the ultramafic association section, with notably higher displacement observed in the Z direction compared to the Y direction. While displacement in the Y direction appears relatively uniform, the total magnitude in the rock type-II surpasses that of the rock type-I portion.

Fig.13 [Images not available. See PDF.]

The displacement magnitude along rock type-II in tunnel route

High convergence values along the invert and sidewalls Fig. 14 highlight the urgent need for support installation post-excavation. Joints and discontinuities create weak zones where stress concentrations can cause increased deformation and collapse risk. Variations in mineral composition Fig. 1 may affect rock brittleness and stability. Therefore, tunnel stability analysis and support installation must account for rock type, discontinuities, and tectonic history, especially in the challenging Himalayan environment [54]. The stress-strength factor is crucial for tunnel stability in underground mining and tunneling. Its neglect has resulted in numerous roof fall fatalities in Indian underground mining. Thus, incorporating this factor into tunnel design and support systems is essential to mitigate accident risks and ensure the safety of underground operations [55]. In the Himalayan region, known for its high squeezing, jointing, and faulting, these geological complexities significantly challenge tunnel stability. The area's tectonic history further impacts rock mass integrity, contributing to stress redistribution during tunnel excavation Fig. 15.

Fig.14 [Images not available. See PDF.]

The convergence of tunnel along rock type-II

Fig. 15 [Images not available. See PDF.]

The stress-Strength ratio along rock type-II

A thorough evaluation of rock mass properties, such as rock type, structure, and geological discontinuities, is crucial for accurately assessing stress accumulation and deformation risks. Structural tunnel design should be aligned with geological conditions to mitigate instability, integrating geological data to optimize alignment, excavation methods, and support system configurations. Bieniawski's approach Table 4 [51] highlights the need to adapt support systems according to geological classifications, enabling a proactive response to changing conditions during the tunnel's lifespan. This adaptation is key to enhancing tunnel resilience against geological hazards.

Table 4. Rock mass classifications and support measures [51]

RMR89 value	Rock class	Support
80–100	Very good	Generally, no support required
60–80	Good	Bolts in crown 3 m long, 2.5 m spacing, 50 mm shotcrete in crown
40–60	Fair	Bolts 4 m long, 1.5–2 m spacing in crown and walls, 50–100 mm shotcrete in crown and 100 mm in wall
20–40	Poor rock	Bolts 4–5 m long, 1–1.5 m spacing in crown and wall, 100–150 mm shotcrete in crown and 100 mm in wall

Conclusions

Based on the analysis of stress distribution, deformation patterns, and displacement magnitudes in tunnel stability assessment, the following conclusions can be drawn:

• Combined kinematic and numerical analyses raise significant concerns about tunnel stability in the Himalayan region, with a 20% probability of wedge failure. Numerical analysis using Hoek–Brown parameters shows increased stress levels, particularly at the tunnel crown along rock type II. Convergence measurements reveal inward displacement trends, particularly at the crown and sidewalls.

• The analysis shows greater displacement at the tunnel crown (1.2 mm) than the walls (0.25 mm), highlighting deformation vulnerability. High shear stress near the crown and side walls, coupled with geological discontinuities, intensifies instability risks in rock type II sections.

• A well-informed support system, combined with a thorough evaluation of stress, deformation data, rock mass properties, and design criteria, is critical for ensuring tunnel stability, as recommended by Bieniawski's modified support system.

• The discussion highlights the complex interplay of factors affecting tunnel stability, including geological characteristics like rock type and discontinuities, as well as external forces. Rock type significantly influences stability, with variations in mineral composition affecting rock mass brittleness and potential stability issues. Additionally, the stress-strength factor is crucial for preventing fatal accidents

Recommendations

Future studies should prioritize the assessment of rock brittleness in Himalayan tunneling projects to enhance stability and safety. Incorporating detailed brittleness evaluations will optimize support systems and mitigate potential risks.

Author contributions

All authors contributed to the study conception and design. Experiments, material preparation, data collection, analysis and numerical modelling were performed by N.A. K.L. M.Z.E. and Y.F. W.L. Methodology, formal analysis, investigation, writing of original draft, visualization, software was performed by N.A. Z.G. Y.F. N.S.C. B.O.T. and J.K. S.H. Conceptualization, validation, resources, writing review and editing, supervision, project administration done by M.S. K.L. N.S.C. N.R.C and J.K. "

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Data availability

The data will be available up on reasonable request from the corresponding authors.

Declarations

Ethics approval and consent to participate

Authors state that the research was conducted according to ethical standards.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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