Research on Mechanical Characteristics and Failure Modes of Interbedded Rock Mass with Varying Dip Angles under High In-Situ Stress

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Focusing on the Jianshan Tunnel along the Zhonglan section of the Yinlan High-Speed Railway, we integrated field testing, laboratory experiments, and numerical simulations to analyze the mechanical response of interbedded rock masses at varying dip angles under high stress. Key findings include:①Field stress measurements at 342.57 m depth revealed a maximum horizontal principal stress of 12.40 MPa, with principal stress relationships SH > SV > Sh;②Laboratory tests demonstrated that the mechanical properties of interbedded rock masses are governed by the soft layer at low dip angles, by the interfacial planes at medium angles, and by the hard layer at high angles, exhibiting distinct failure modes: tensile splitting, shear failure, and composite failure, respectively;③ Numerical simulations classified surrounding rock deformation into four zones based on horizontal displacement evolution: slow-development, rapid-development, stabilization, and attenuation zones, with peak asymmetric displacement occurring at medium dip angles where minor eccentric tension and major eccentric compression regions form in supporting structures. These results provide critical insights for deformation control technologies and analogous engineering projects. Physical sciences/Engineering Physical sciences/Materials science Earth and environmental sciences/Solid earth sciences High in-situ stress interbedded tunnel mechanical characteristics failure modes discrete element analysis 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 1. Introduction Due to the complex terrain, hydrogeological conditions, and inherent characteristics of rock formations in western China, tunnel construction in the region is evolving toward greater depth, length, scale, difficulty, and risk 1 – 3 . During the construction of layered soft rock tunnels in high-altitude areas of western China, engineers face not only challenges such as weak self-stabilization capacity, poor mechanical properties, and water-induced softening of layered rock masses but also multiple stressors including high water pressure, fault-fold structures, and combined tectonic and gravitational stress fields. Consequently, the stress distribution within the surrounding rock-support structure system becomes exceptionally complex, leading to frequent hazards such as support deformation and cracking, extrusion-induced large deformations 4 – 5 , high-stress rockbursts 6 – 7 , and water inrushes 8 – 9 . These challenges pose significant difficulties for tunnel design, construction, and subsequent operation and maintenance in western China.Due to the more complex mechanical properties and failure modes of interbedded hard-soft rock masses under varying layer thicknesses and dip angles, the deformation mechanisms of tunnels in such strata under high in-situ stress remain inadequately understood, and deformation control poses greater challenges. This necessitates in-depth systematic investigation 10 – 12 . Current research on tunnels in stratified rock masses primarily focuses on their physical-mechanical properties, stability, and deformation characteristics. Zhang et al. 13 investigated the deformation and failure mechanisms of multilayered rock masses using triaxial rheological tests, revealing three dominant failure modes: monoclinic shear failure, tensile crack failure, and interfacial shear-slip failure.Sher 14 employed the three-dimensional boundary element method to determine the stress state of fractured elastic rock masses, establishing the influence of stratified rock strength characteristics on the geometry, dimensions, and area of radial fractures. Crucially, it was demonstrated that fracture morphology can be modified by adjusting the explosive distribution along boreholes.Chekhov 15 developed an exact analytical approach based on three-dimensional nonlinear theory to investigate surface instabilities in regularly stratified semi-infinite media, providing a rigorous framework for assessing the stability of layered rock formations.Fereshtenejad et al. 16 proposed a practical 3D geometric modeling method for simulating folded rock strata, motivated by the recognition that planar assumptions in prior studies of rocks with curved discontinuities introduce significant errors in subsequent analyses. Their approach utilizes MATLAB scripts to generate optimized input data for mechanical analysis.Triantafyllidis et al. 17 addressed layered rock failure by assuming orthotropic elasticity in components prior to failure. They evaluated local stress-strain states and integrated multiple failure criteria to develop a comprehensive framework encapsulating 3D elasticity and failure mechanisms, validated through case studies elucidating the model's mechanical responses.Berti et al. 18 addressed the challenge of determining physical-mechanical properties in flysch—a sedimentary rock characterized by soft-hard interbedding. By analyzing large-scale landslides in Cretaceous flysch formations, they compared failure strengths with those predicted using an enhanced Geological Strength Index (GSI) methodology.Bonilla-Sierra et al. 19 integrated photogrammetry and Discrete Fracture Network (DFN)techniques with the Discrete Element Method (DEM). Utilizing the SiroVision 3D mapping system and its structural mapping tools, they imported case-specific geotechnical data of unstable strata into computational models for stability analysis of pre-fractured rock masses.Li et al. 20 conducted indoor experiments on soft hard interlayered rock samples in the Jinping area and analyzed three failure modes caused by different distribution forms of weak layers under uniaxial compression, as well as the deformation and failure characteristics of rock samples under different loading paths under biaxial compression. They further studied the influence of the dip angle, quantity, distribution form, and volume ratio of weak layers on the strength characteristics. Studies by the aforementioned experts indicate that research on the mechanical properties and failure modes of layered rock masses has primarily focused on analyzing physical-mechanical characteristics and failure patterns through laboratory experiments considering different rock mass properties. However, integrated approaches combining laboratory testing with discrete element analysis remain scarce. Therefore, this study conducts laboratory experiments to analyze the mechanical behavior and failure mechanisms of interbedded rock masses at varying dip angles, and employs discrete element modeling (DEM) to comparatively investigate surrounding rock displacement, support loading, and crack propagation in tunnels constructed within such strata. This integrated methodology aims to offer insights for the construction and support design of interbedded rock tunnels under high in-situ stress conditions. 2. Engineering Overview 2.1 Engineering background The Yinlan High-speed Railway Zhonglan section spans a total length of 219.671 km, with newly constructed double-track tunnels measuring 50.626 km across 25 tunnels, accounting for 23.0% of the total route length. Among these, the Xiangshan Tunnel and Jianshan Tunnel are key projects of the entire line. The Jianshan Tunnel extends from chainage DK109 + 780 to DK115 + 782, with a total length of 6,002 m. It is the longest tunnel on the Zhonglan Passenger Dedicated Line (Gansu Section) and the only water-abundant tunnel along the entire route. The design elevation of the tunnel entrance shoulder is 1,356.34 m, while the exit shoulder elevation is 1,640.08 m, featuring a unidirectional longitudinal grade. The entrance construction section spans 2,075 m with a maximum burial depth of 519 m. The tunnel body traverses 7 fault zones, posing risks of sudden collapse and presenting extremely high construction challenges and safety risks. The lithology of the strata in this area is relatively complex, dominated primarily by sedimentary and metamorphic rocks, with exposed formations comprising Quaternary unconsolidated deposits; Jurassic Middle Series Honggou Formation sandstone interbedded with mudstone; Devonian Lower-Middle Series Xueshan Group sandstone interbedded with conglomerate; Silurian Lower Series Magouying Formation metamorphic sandstone interbedded with phyllite; and alternating beds of metamorphic sandstone and mudstone within the Silurian Lower Series Magouying Formation, all of which consist of unweathered rock. The rock strata exhibit steep inclination, with their strike essentially parallel to the tunnel axis. The surrounding rock conditions at the tunnel face are illustrated in Fig. 1 . 2.2 Analysis of In-situ Stress Measurement Results Considering comprehensive factors including on-site engineering geological conditions, specialized testing agencies were collaboratively engaged to conduct two separate hydraulic fracturing stress measurements at specific locations within the Jianshan Tunnel during distinct time periods (Fig. 2 ). A borehole was drilled at chainage DK113 + 710 near the tunnel axis elevation for the initial stress measurement. As per engineering design specifications, the planned final borehole depth was 274.91 m. However, during testing operations, severe borehole wall collapse and rock fragmentation occurred, limiting instrument penetration to approximately 163 m. Through technical coordination, stress measurements were successfully conducted in the accessible section above the obstruction point (~ 163 m). Within the 99–163 m depth interval, data from 12 measurement segments were successfully acquired, with 8 segments yielding well-defined maximum and minimum horizontal principal stress values. Using fracturing parameters - including breakdown pressure reopening pressure, and instantaneous shut-in pressure - the maximum (SH) and minimum (Sh) horizontal principal stresses were calculated. The computational results, along with vertical stress (Sv) values, are detailed in Table 1 . Table 1 In-situ Stress Measurement Results Table for Borehole D2Z-Jian-15, Jianshan Tunnel. No. Interval Depth(m) Fracturing Parameters (MPa) Principal Stresses (MPa) λ σ H Orientation (°) P b P r P s P 0 T S H S h S v 1 99.67 2.78 2.41 1.50 0.97 0.37 3.12 2.50 2.69 1.16 2 107.88 3.14 2.62 1.71 1.05 0.52 3.62 2.79 2.91 1.24 3 117.2 3.32 2.72 1.59 1.14 0.60 3.27 2.77 3.16 1.03 4 126.48 4.11 3.22 1.92 1.23 0.90 3.84 3.19 3.41 1.12 5 131.18 4.19 3.58 2.12 1.28 0.62 4.13 3.43 3.54 1.17 N12°E 6 141.65 3.71 2.72 1.92 1.39 0.99 4.47 3.33 3.82 1.17 7 150.86 4.93 3.70 2.15 1.48 1.23 4.27 3.65 4.07 1.15 N23°E 8 155.46 5.12 4.30 2.39 1.52 0.83 4.45 3.94 4.20 1.06 P b -In-situ rock fracture initiation pressure; Pr -Fracture reopening pressure༛ Ps -Fracture closure pressure༛ P 0 -Formation pore pressure at measurement depth༛ T -Rock tensile strength༛ S H -Aximum horizontal principal stress; S h -Minimum horizontal principal stress༛ S V -Overburden stress (calculated with rock density 2700 kg/m³). As evidenced in Table 1 , the magnitude relationship among the three principal stresses exhibits S H > S V > S h .The maximum horizontal principal stress exceeding the vertical stress indicates a predominantly horizontal stress regime in the vicinity of the borehole. The lateral pressure coefficient ( S H / S V ) ranges from 1.03 to 1.24, with a mean value of 1.14. This is significantly higher than the lithostatic pressure coefficient (generated solely by overburden weight) , demonstrating that the in-situ stress field within the measurement depth is subject to the collective influence of tectonic stresses and topographic valley effects. The hydraulic fracturing stress measurement results indicate that:The in-situ stress field in the Jianshan Tunnel area is primarily controlled by tectonic stresses;The surrounding stress regime exhibits NE-oriented compressive stresses; Horizontal stresses dominate throughout the region. For the second test, hydraulic fracturing was again employed to conduct in-situ stress measurements in the Jianshan Tunnel. The selected test location was at chainage DK113 + 400, with the borehole collar approximately 310 m below ground surface and a drilling depth of 35.2 m. Based on initial data including geological conditions, Rock Quality Designation (RQD) of core samples, and borehole sediment, bottom-up stress testing was conducted at three intervals. However, only two sets of reliable data were obtained from measurement depths of 28.43 m and 32.57 m.The pressure recording curves for the measurement intervals are presented in Fig. 3. Table 2 Characterization Parameters of Fracturing and Calculated In-situ Stresses. No. Interval Depth(m) Fracturing Parameters (MPa) Principal Stresses (MPa) σ H Orientation (°) P b P r P s P 0 T S H S h S v 1 28.43 9.55 8.86 6.49 0.28 0.69 10.89 6.77 8.97 N40.6°E 2 32.57 7.90 7.64 6.57 0.33 0.26 12.40 6.90 9.08 N27.3°E According to the Table 2 , at a depth of 342.57 m:Maximum horizontal stress comes to 12.40 MPa;Saturated uniaxial compressive strength R c <30 MPa (classified as soft rock).When = 2–4 ,belong to high in-situ stress conditions;When < 2, belong to extremely high in-situ stress conditions.Therefore, there is high ground stress at the deeper part of the Jianshan Tunnel, and the possibility of rock burst during construction is low. There is a possibility of soft rock deformation and damage, mainly due to accidents such as roof caving. 3. Study on Mechanical Properties of Interbedded Rock Masses 3.1 Sampling of Interbedded Rock Masses To analyze the fundamental characteristics of in-situ interbedded rock samples, core sampling was conducted at the high-stress section DK112 + 160, based on:Geological reconnaissance within the tunnel zone and In-situ stress measurements from Jianshan Tunnel. The sampled lithology primarily consists of sandstone-mudstone interbeds. Specimens were extracted through precision coring for laboratory testing under multiaxial stress conditions (Fig. 4 ). To investigate the compression failure modes of soft-hard interbedded rock masses under different bedding dip angles, five groups of standard cylindrical specimens (50 mm in diameter and 100 mm in height) were prepared at varying dip angles. Each group contained no fewer than four specimens with dip angles of 0°, 30°, 45°, 60°, and 90° respectively. The sampling method is illustrated in Fig. 5 , while specimens with different dip angles are shown in Fig. 5 . The sandstone layers (primarily 1–2 cm thick) exhibited relatively high strength, whereas the mudstone layers (mainly 0.5-1 cm thick) showed lower strength. All specimens exhibited distinct interbedding features. The prepared specimens were systematically numbered according to their dip angles to facilitate subsequent data recording during uniaxial and triaxial compression tests, as well as for post-failure pattern observation (Fig. 5 ). The numbered specimens were subjected to uniaxial and triaxial compression tests using a YAW-2000M multifunctional rock testing system (Fig. 6 ) in the rock mechanics laboratory. This apparatus features high stability and precise control accuracy. 3.2 Analysis of Uniaxial Compression Results for Interbedded Rock The uniaxial compression test results for interbedded rock specimens with varying dip angles are presented in Fig. 7 . From Fig. 7 , it can be seen that the stress-strain curves of specimens with different angles of soft and hard interlayers mainly consist of five stages: 1) primary compaction stage: in this stage, the stress-strain curve shows a slightly upward bending trend, and there are basically no cracks appearing on the surface of the rock mass; 2) Elastic development stage: In this stage, the stress-strain curve shows an oblique linear rise, accompanied by a continuous increase in load. Cracks have already appeared inside the rock, and there are also subtle cracks on the surface. In this stage, the cracks are not obvious but have already appeared and continued to develop (Fig. 8 (a)); 3) Strain hardening stage: During this stage, the stress-strain curve shows a significant nonlinear change, and the number of cracks increases significantly, mainly shear cracks accompanied by the appearance of tensile cracks (Fig. 8 (b)); 4) Strain softening stage: After the uniaxial compressive bearing capacity reaches its peak, the actual internal structure of the component has been destroyed, and most of the specimens can still maintain a basic stable shape. The stress decay rate is very fast, and the crack development rate increases, rapidly expanding and connecting into a fracture surface (Fig. 8 (c)); 5) Post peak residual stage: In this stage, the stress-strain curve of the specimen shows a significant and rapid decrease due to its failure, basically dropping to 0. Macroscopically, it is manifested as block slip of the rock mass (Fig. 8 (d)). From Fig. 7 , it is also found that the stress-strain curves of different inclination angles show brittle failure. At lower inclination angles (0 °~30 °), the strain corresponding to the peak strength of the specimen is usually between 0.4% and 0.5%; When the inclination angle is moderate (45 °~60 °), the strain corresponding to the peak strength of the specimen is usually between 0.2% and 0.3%; When the inclination angle is large (90 °), the strain corresponding to the peak strength of the specimen is usually between 0.5% and 0.6%. That is to say, the strain required for the specimen to reach the peak strength at a medium inclination angle is smaller, resulting in faster structural failure. In addition, during the process of the inclination angle from 0 ° to 60 °, the peak uniaxial compressive strength decreases continuously. When the inclination angle is 0 °, the compressive strength is 14.28 MPa; When the inclination angle is 30 °, the compressive strength is 11.65 MPa, with a decrease of 18.42%; When the inclination angle is 45 °, the compressive strength is 7.3 MPa, with a decrease of 48.88%; When the inclination angle is 60 °, the compressive strength is 4.6 MPa, with a decrease of 67.79%. When the inclination angle changes from 60 ° to 90 °, the uniaxial compressive strength increases to 14.02 MPa, slightly lower than the compressive strength at 0 °. From the above data, it is not difficult to see that the layered rock mass has obvious anisotropy. Further analysis reveals that:At low dip angles (0°–30°), the axial strain tends to be relatively large, and a certain amount of strain persists even in the post-peak residual stage. In interbedded rock masses, the soft layers typically exhibit low elastic modulus and overall lower strength, indicating that the mechanical behavior of the interbedded rock is primarily governed by the soft layersin this range.At medium dip angles (45°-60°), failure of the interbedded rock mass mainly manifests as sliding failure, predominantly along the interfaces between soft and hard layers. This suggests that the mechanical properties are dominated by the soft-hard interlayer interfaces in this range.At high dip angles (90°), the load is jointly borne by both the soft and hard layers. However, due to the higher strength of the hard layers, the mechanical behavior of the interbedded rock mass is predominantly controlled by the hard layers in this case.Even after the axial stress drops in the post-peak residual stage, a certain residual strength is retained. This is because: Crack propagation may exhibit nonlinear characteristics, meaning the rock mass is not entirely destroyed internally.Alternatively, complete failure may be confined to a specific layer (often the soft layer), while the specimen as a whole remains partially intact, allowing it to retain some load-bearing capacity. 3.3 Analysis of Triaxial Compression Results for Interbedded Rock Mass Based on in-situ stress measurements, the confining pressures in this triaxial test were set at 5 MPa, 10 MPa, and 15 MPa. The stress-strain relationship curves under varying confining pressures and dip angles during the test are shown in Fig. 9 . From Fig. 9 (a), it can be observed that in triaxial tests under 5 MPa confining pressure, specimens with different dip angles exhibit varying post-peak residual strengths after reaching peak strength. Specifically, specimens with small dip angles (0°, 30°) and large dip angles (90°) show higher post-peak residual strengths, whereas those with medium dip angles (45°, 60°) exhibit lower post-peak residual strengths. In the later stage of strain, the rock mass demonstrates certain ductile characteristics at small and large dip angles, while at medium dip angles, it displays some brittle features. Overall, under confining pressure, the stress-strain behavior of interbedded rock specimens varies to some extent depending on the dip angle.. A comparison of the three diagrams in Fig. 8 reveals that under low confining pressure, the stress of the interbedded rock mass drops rapidly after reaching peak strength, exhibiting significant softening characteristics. When the confining pressure is increased, the post-peak stress decreases more gradually with increasing strain, and the strain softening phenomenon progressively weakens. In the later stage of strain, the interbedded rock mass demonstrates ductile failure characteristics. Furthermore, by comparing the stress-strain curves of specimens with the same interbedding dip angle under different confining pressures, it can be observed that high confining pressure promotes a transition from brittle to ductile behavior in both small-dip and large-dip rock masses. However, this change is not particularly pronounced in interbedded rock specimens with medium dip angles. 3.4 Analysis of Failure Modes in Uniaxial Compression of Interbedded Rock Masses The stability of rock is closely related to the distribution and propagation of cracks on its surface and within its internal structure. Typically, rock instability is caused by crack propagation and the interconnection of different cracks. Studying the failure modes of interbedded specimens under compression helps to fundamentally clarify the failure mechanisms of interbedded rock. During uniaxial compression tests, audible cracking sounds were observed in interbedded specimens of all dip angles upon failure, and their stress-strain curves exhibited distinct brittle characteristics. The failure patterns are illustrated in Fig. 10 . The location and propagation pattern of cracks play a decisive role in the ultimate failure mode of rock masses. As can be observed from Fig. 10 : For specimens with small dip angles (predominantly 0°, with a few at 30°), due to their high peak strength and elastic modulus, cracks find it difficult to propagate in the soft-hard interbedded rock mass because the soft layers exhibit certain ductility. Consequently, failure typically initiates in the hard layers and gradually extends to the soft layers, ultimately forming vertical fissures that penetrate both the soft and hard strata. Additionally, due to the deformation incompatibility between the soft and hard layers, the soft layers may undergo compressive deformation first, generating transverse forces at their interfaces. Under these transverse forces, tensile cracks perpendicular to the force direction develop and propagate in the interbedded rock mass. The resulting cracks are vertical tensile cracks that penetrate the entire soft-hard bedding planes (Fig. 10 (a)), characteristic of splitting failure. The moderately inclined rock specimens (mainly at 45°, with some at 60°) exhibit relatively low peak strength and elastic modulus. During compression, the interbedded specimens with moderate inclination experience some slippage between the soft and hard layers. Due to the larger inclination angle of these moderately interbedded specimens, the slippage phenomenon is more pronounced. When the interface between the soft and hard interbeds can no longer withstand the shear stress, sliding failure occurs. At this stage, the oblique cracks are predominantly shear cracks, with fewer tensile cracks. The cracks generated in the rock mass are oblique cracks that penetrate the entire soft-hard bedding plane (Fig. 10 (b)), indicating a shear failure mode. High-angle rock specimens (predominantly 90°, with a few at 60°) exhibit a combined failure mode due to the simultaneous compression of both soft and hard layers. However, the difference in their elastic moduli leads to uneven deformation rates, promoting crack propagation and the formation of fracture surfaces. Under the combined action of tensile stress and shear stress, the cracks develop into vertical tensile fractures and inclined shear cracks. The resulting fractures in the rock mass represent a composite failure mode, combining tensile splitting (cleavage) and shear slippage (Fig. 10 (c)), thus classifying it as a mixed failure mechanism. Under uniaxial compression, interbedded rock specimens with varying dip angles exhibit three primary failure modes: splitting (tensile) failure, shear failure, and composite failure. Observations of the failure patterns reveal that in interbedded rock masses, the soft layers, due to their higher ductility, tend to inhibit crack propagation, resulting in slower fracture development. This suggests that increasing the thickness of soft layers in soft-hard interbedded rock masses can, to some extent, suppress crack coalescence and the formation of macroscopic fracture surfaces, thereby enhancing the overall stability of the rock mass. 3.5 Analysis of Triaxial Compression Failure Modes in Interbedded Rock Masses Under triaxial compression tests, the ultimate failure modes of soft-hard interbedded rock masses with different dip angles are shown in Fig. 11 . In addition to the influence of dip angles, the application of varying confining pressures leads to distinct characteristics in the failure patterns, crack propagation trends, and coalescence forms of the interbedded rock masses. As can be seen from Fig. 11 , there are certain differences in the failure modes of soft-hard interbedded rock specimens with different dip angles under varying confining pressures. Under triaxial compression, as the confining pressure increases, shear failure becomes more prevalent in the rock mass. Additionally, due to the distinct physical and mechanical properties of soft and hard layers, the constraining effect of confining pressure on the expansive deformation of soft layers is significantly weaker than that on hard layers. This leads to deformation incompatibility between soft and hard layers under confining pressure. Coupled with the cohesive forces between the layers, the soft layers, which undergo greater expansion, experience volumetric swelling. As a result, misaligned sliding occurs between the soft and hard interbeds, leading to shear failure in the interbedded rock specimens. Therefore, under low confining pressure: For small-dip-angle interbedded specimens, the failure mode primarily involves tensile cracks localized in the hard layers, with overall splitting failure dominating. Vertical cracks appear on the specimen surface, and while the failure is incomplete, the specimen retains some integrity (Fig. 11 (a)). For medium-dip-angle specimens, localized tensile cracks occur, along with inclined cracks penetrating the entire specimen. Shear failure dominates, and the destruction is more thorough (Fig. 11 (b)). For large-dip-angle specimens, the failure mode features inclined cracks running through the entire rock mass, primarily exhibiting shear failure. The destruction is relatively thorough, though the failure location differs somewhat from that of medium-dip-angle specimens (Fig. 11 (c)). When the confining pressure increases, the soft-hard interbedded rock specimens with different dip angles are more prone to shear failure. At this point, regardless of whether the specimens have a small, medium, or large dip angle, inclined cracks are observed. Under high confining pressure, small-dip-angle interbedded specimens exhibit longitudinal, slightly inclined cracks penetrating the entire sample. These cracks consist of a main fracture and several minor cracks. The primary failure mode is splitting failure, with minimal overall fragmentation, allowing the specimen to maintain its integrity. For medium-dip-angle interbedded specimens, the dominant failure mode includes inclined cracks traversing the entire specimen, along with a few vertical and horizontal cracks. The failure is mainly a combination of shear and splitting failure. The inclined cracks propagate rapidly, forming large, continuous fracture surfaces. During failure, rock debris is generated, leading to severe damage and a loss of self-stability. In large-dip-angle specimens, the failure primarily manifests as localized inclined cracks, with crack size and propagation speed decreasing as confining pressure increases. The dominant failure mode is shear failure, producing wide cracks that do not fully connect into a continuous fracture surface. As a result, the rock mass retains its self-stability. From the triaxial test results, unlike uniaxial compression tests, although the soft layers in soft-hard interbedded rock masses still inhibit crack propagation, this inhibitory effect does not increase linearly. When the thickness of the soft layers varies within a certain range, their influence on crack extension is most pronounced. If the soft layer thickness falls outside this range, two scenarios may occur: ① When the soft layer thickness exceeds this range, the skeletal structural effect formed by the inherent physical and mechanical properties of the hard layers diminishes. Additionally, due to the larger thickness of the soft layers, the spacing between hard layers increases, weakening stress transfer. As a result, the proportion of stress borne by the hard layers decreases, while the soft layers bear higher stress. However, under triaxial conditions, the confining pressure restricts the expansive deformation of the soft layers, preventing stress release and leading to crack initiation. ② When the soft layer thickness is below this range, the thin soft layers fail to provide sufficient stress buffering, reducing the overall stability of the rock strata. Consequently, cracks interconnect and coalesce, forming fractures. 4. Deformation Characteristics of Interbedded Tunnels Based on Discrete Element Analysis 4.1 Overview Previous studies investigated the mechanical properties and failure modes of interbedded rock masses under uniaxial and triaxial compression through laboratory tests. However, as a complex geological material, rock inherently contains numerous defects. With the increase in scale of rock engineering, research focus has gradually shifted from intact rock to jointed and fractured rock masses. In practical engineering, evaluating the mechanical stability of rock masses and the structural safety of tunnels requires analysis of rock strength, deformation and failure characteristics, as well as crack propagation behavior. Rock masses are often intersected by multiple joints or structural planes, making them unsuitable for treatment as continuous media in certain cases. Due to their pronounced discontinuities, conventional continuum mechanics methods (such as the finite element method) may prove inadequate. In such scenarios, the discrete element method (DEM) offers a more rational approach for analyzing discontinuous media, particularly for jointed rock masses. 3DEC (3 Dimension Distinct Element Code) is the abbreviation for a three-dimensional discrete element method program. Building upon the core principles of UDEC, it extends the two-dimensional planar discrete medium mechanics into three-dimensional space. As a program based on the discrete element method (DEM), 3DEC describes the mechanical behavior of discontinuous media. It adopts the same finite difference approach as FLAC while incorporating simulations of discontinuous behavior at contact interfaces in terms of mechanics. 4.2 Model Establishment and Parameter Selection The following assumptions were adopted in the numerical modeling and analysis of this study: (1) The surrounding rock contains only joints with a single orientation and uniform mechanical properties; (2) In the computational model, the constitutive models for blocks and joint elements are transversely isotropic and zone-contact elastoplastic (based on Coulomb slip failure), respectively; (3) The influences of groundwater and temperature fields are not considered; (4) Secondary lining structures are excluded from the calculation process as a safety reserve. The discrete element model was established using 3DEC 7.0 software. Based on the results of discrete element numerical analyses from relevant previous literature and engineering accuracy requirements[21–22], while balancing computational efficiency and result precision, the overall model dimensions were ultimately determined as 100m (length) × 100m (width) × 30m (height). The upper surface was defined as a free boundary, with displacement constraints applied to all other surfaces. Boundary forces were applied according to in-situ stress measurement results from the tunnel site. To address computational challenges associated with the discrete element method (including large calculation volumes, numerous elements, and time-consuming processes), the model was appropriately simplified based on field geological investigations. The central 50m × 50m area of the model was designated as interbedded hard rock (sandstone) and soft rock (mudstone), while surrounding regions were modeled as homogeneous, non-interbedded Grade V rock mass. Multiple discrete element models were developed within the central zone with varying hard/soft layer thickness ratios and dip angles. Tunnel excavation was simulated using the three-bench method, as illustrated in Fig. 12 . The mechanical parameters adopted for the layered rock mass in this study are presented in Table 2 . Table 2 Rock Mechanics Parameters. Rock Mas Unit Weight γ /kN.m − 3 Elastic Modulus E /GPa Poisson's Ratio µ Internal Friction Angle ϕ /。 Cohesion c /MPa Hard Rock 2250 5.10 0.30 36 12.0 Soft Rock Grade V Surrounding Rock 2000 1800 1.30 1.50 0.35 0.39 15 22 0.51 0.12 The shotcrete employs C25-grade concrete, with steel frames consisting of I20-section steel members. The mechanical parameters of the primary support and steel frames are detailed in Table 3 . Table 3 Primary Support Parameters Table. Material Type Thickness d /cm Elastic Modulus E /GPa Unit Weight γ /kN.m − 3 Poisson's Ratio µ C25 Shotcrete + Steel Frame 25 25.6 2400 0.2 Φ22 rock bolts are employed, with detailed specifications provided in Table 4 . Table 4 Anchor Bolt Parameters. Length/m Area A/m 2 Elastic Modulus E/GPa Grout Stiffness k/GPa Bond Strength s/MPa 3.5 3.8e-4 200 8.75 6.91 4.3 Discrete Element Result Analysis (1) Surrounding Rock Displacement Models were established with a hard rock to soft rock thickness ratio of 1:1,The reason for selecting a 1:1 thickness ratio in the model and its rationale, within the proportion range of soft-to-hard interbedded rock layers measured by field sampling. The dip angles selected for analysis correspond to those used in laboratory tests, namely 0°, 30°, 45°, 60°, and 90°. The numerical models for each case are shown in Fig. 13 . The displacement nephograms under high in-situ stress conditions for varying interbedded dip angles are presented in Fig. 14 (using 0° and 60° cases as representative examples). As shown in Fig. 15 : When the bedding planes of the interbedded rock mass are horizontal, the vault settlement reaches its maximum value of 268.84 mm. The softening effect of soft layers results in a lower deformation modulus of the soft-hard interbedded rock mass. With horizontal bedding, the tensile-bending resistance at the vault is relatively weak. Under significant overburden depth, the self-weight of the overlying rock mass tends to cause unilateral flexural failure, leading to substantial vertical deformation in the surrounding rock. The vault settlement exhibits a decreasing trend within the 0°–45° inclination range but increases within the 45°–90° range. This indicates that as the interbedded rock transitions from low to medium dip angles, the increase in inclination reduces tensile-bending effects, resulting in relatively smaller vault displacement. However, when the rock mass shifts from medium to high dip angles, bedding-plane slip drives continuous displacement growth. At medium dip angles, the mechanical behavior of the interbedded rock becomes more complex, potentially involving simultaneous tensile-bending and bedding-plane slip—a finding consistent with laboratory test results. Due to the effect of high in-situ stress, the maximum horizontal displacement of the surrounding rock is significantly greater than the vertical displacement. As shown in Fig. 16 : As the dip angle of interbedded layers increases, the displacement at the left haunch first decreases and then increases. The inclination of rock layers not only causes the left surrounding rock to tend to slide away from the free surface, but also induces mutual compression between rock masses, potentially leading to stress concentration. Conversely, the displacement at the right haunch initially increases slowly and then decreases with increasing dip angle. Larger dip angles amplify bedding-plane slip in the surrounding rock. Additionally, given the lower tensile and shear strength of soft rock layers, plastic flow becomes more likely at steeper angles, resulting in extrusion displacement. Figure 16 categorizes the asymmetric deformation of interbedded rock masses under high in-situ stress into four distinct zones based on displacement disparities between left and right haunches:Slow Progression Zone of Asymmetric Deformation;Rapid Development Zone of Asymmetric Deformation;Stabilization Zone of Asymmetric Deformation;Mitigation Zone of Asymmetric Deformation 0°–30° dip range: Asymmetric deformation initiates from symmetrical displacement (observed at 0° horizontal bedding). This phase exhibits gradual asymmetric progression with emerging yet limited displacement differences between left and right haunches. 30°–45° dip range: Asymmetric deformation undergoes accelerated development, peaking at 45° where the displacement disparity reaches its maximum. 45°–60° dip range: Post-peak asymmetric deformation shows slight decline at a subdued rate, maintaining overall stability within a defined range. At 60°, significant displacement differences persist between both haunches. 60°–90° dip range: A pronounced mitigation trend emerges in asymmetric deformation. By 90° (vertical bedding), haunch displacements become nearly symmetrical—exhibiting negligible difference similar to the 0° horizontal condition. (2) Support Forces The stress nephograms of the primary support structure under different dip angles are shown in Fig. 17 , with 30° and 45° taken as examples here. As can be seen from Fig. 17 , when the interbedding dip angle is 30°, the support structure is subjected to a maximum tensile stress of 2.33 MPa and a maximum compressive stress of 18.32 MPa; at a dip angle of 45°, the maximum tensile stress is 1.65 MPa, and the maximum compressive stress reaches 20.72 MPa. To more intuitively analyze the support forces at different locations of the tunnel under varying interbedding dip angles, the numerical simulation results at each point were extracted and summarized, as shown in Fig. 18 below. From Fig. 18 , the following observations can be made: ① Regarding the maximum principal stress of the supporting structure, the stress at the vault reaches 2.57 MPa at 0°. The stress at the vault varies only slightly with the inclination angle, showing an initial decrease followed by an increase. ② For the left and right arch shoulders and the left and right arch haunches of the supporting structure, the stress fluctuates significantly with the inclination angle. The maximum tensile stress difference occurs at the arch shoulders between 45° and 60°. However, since the overall tensile stress values are relatively small, this region is classified as a minor eccentric tension zone. ③ The stresses at the left and right arch haunches follow a similar trend with changing inclination angles, but the maximum compressive stress difference occurs within the 30°–60° range. This area covers a wide range with a substantial stress difference, making it a major eccentric compression zone. ④ The stresses at the left and right arch shoulders and the left and right arch haunches also exhibit asymmetry. The maximum stress differences reach 0.43 MPa and − 1.21 MPa, respectively, indicating that in interbedded hard and soft strata, medium inclination angles lead to a stress state dominated by eccentric compression with supplementary eccentric tension. ⑤ The stresses at the vault and right arch haunch are the highest, bearing greater surrounding rock pressure. Therefore, during construction, in addition to pre-reinforcement in high-stress areas, the timing of support installation must be carefully controlled to prevent excessive pressure on the supporting structure, which could lead to damage. (3) Crack Propagation Analysis As previously discussed, for tunnels in high-stress interbedded soft and hard rock strata, crack development is a critical factor affecting subsequent surrounding rock stability. Crack propagation typically undergoes three stages: nucleation, steady-state growth, and unstable growth. Once cracks enter the unstable propagation stage, irreversible damage occurs to the material, posing significant hazards. Currently, for interbedded soft rock under high stress, most studies rely on finite element analysis, leaving limited research on crack behavior. However, the 3DEC discrete element software can analyze crack distribution and evolution by examining joint opening displacements. Therefore, this section investigates crack distribution under different interbedding angles with equal layer thickness, as illustrated in Fig. 19 (using 45° and 90° as examples). As can be seen from Fig. 19 : Based on a joint opening displacement of 3 mm, the crack distribution under different interbedding dip angles is closely related to the dip angle, with cracks generally propagating parallel to the bedding plane. At a 90° dip angle, all cracks propagate downward, primarily concentrated in the left and right arch shoulders and arch haunches. The maximum crack width reaches 28.11 mm, occurring at the right arch foot. At a 45° dip angle, cracks predominantly follow a 45° trajectory, mainly distributed at the right arch shoulder and the left arch haunch and waist. The maximum crack width reaches 71.65 mm, and the number of cracks is significantly higher than that at the 90° dip angle. Table 4 . Maximum crack length at different dip angles. Interbedding dip angle/° 0 30 45 60 90 Maximum crack length/mm 33.05 41.53 71.65 49.32 28.11 As can be seen from Table 4 , the crack length in the interbedded rock mass generally follows a trend of first increasing and then decreasing with the dip angle, reaching its minimum at 90° and peaking at 45°. The reasons for this pattern are as follows: At 0°–45°, asymmetric deformation develops gradually, but the early-stage deformation progresses relatively slowly, resulting in limited joint crack growth. At medium dip angles (around 45°), shear failure intensifies, and bedding-parallel slip becomes dominant, leading to a sharp increase in crack length. At 45°–60°, asymmetric deformation weakens, and as the dip angle increases, the slip effect diminishes, partially suppressing crack propagation. At 60°–90°, cracks are further constrained, with both crack length and distribution density decreasing, ultimately reaching their minimum at 90°. 5. Conclusions As a composite rock mass composed of multiple media, interbedded rock exhibits significant anisotropic characteristics in deformation and strength, which distinctly differ from those of homogeneous rock masses. The mechanical properties of layered rock are strongly influenced by bedding planes, the mechanical properties of the rock material, and the dip angle of the bedding planes. In this study, laboratory tests were conducted to analyze the mechanical behavior and failure characteristics of interbedded rock masses with different dip angles under high in-situ stress conditions. Additionally, discrete element analysis was employed to investigate the surrounding rock displacement, support loading, and crack propagation in tunnels with interbedded rock layers of varying thicknesses and dip angles. The following conclusions were drawn: (1) The mechanical properties of interbedded rock masses are significantly influenced by the dip angle. At low dip angles, the soft layers dominate the mechanical behavior; at medium dip angles, the interfaces between soft and hard layers play a decisive role; and at high dip angles, the hard layers become predominant. With increasing confining pressure, the post-peak strain softening gradually weakens, and the ductile failure characteristics of the specimens become more pronounced. (2) In uniaxial compression tests, rock masses with small dip angles undergo splitting failure, generating vertical tensile cracks that penetrate the bedding planes.At medium dip angles, shear failure occurs, producing oblique cracks that traverse the bedding planes.At high dip angles, composite failure takes place, forming both vertical tensile cracks and oblique cracks.When the thickness of the soft layer varies within a certain range, its influence on crack propagation is most pronounced. (3) In the triaxial compression test, rock masses with small dip angles undergo splitting failure, with tensile cracks occurring in the hard layers;rock masses with medium dip angles exhibit shear failure, accompanied by localized tensile cracks, but the overall pattern is dominated by inclined cracks;rock masses with large dip angles experience shear failure, generating oblique cracks that penetrate the rock mass. The increase in confining pressure makes interbedded soft-hard rock masses of varying dip angles more prone to shear failure. (4) Using the discrete element software 3DEC, a comparative analysis was conducted on the surrounding rock displacement, support forces, and crack propagation under different dip angles with equal layer thickness. Based on the maximum horizontal displacement difference between the left and right sides, the surrounding rock deformation was divided into four zones: the slow development zone of asymmetric deformation, the rapid development zone of asymmetric deformation, the stable zone of asymmetric deformation, and the weakening zone of asymmetric deformation. It was found that the asymmetric displacement peaks at medium dip angles (30°–60°), forming small tension and large compression zones in the support structure. Additionally, crack distribution is closely related to the dip angle of interbedded layers. Declarations Author Contribution Zhichun Fang, Xinyu Xu wrote the main manuscript text and prepared Figs. 1-19. All authors reviewed the manuscript. Data Availability All data generated or analysed during this study are included in this published article References Li, J. H. et al. Mechanical Properties and Constitutive Model for Soft-Hard Interlayered Rock Mass. 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Investigation Into Deformation and Failure Characteristics of the Soft-Hard Interbedded Rock Mass Under Multiaxial Compression. FRONTIERS IN EARTH SCIENCE.2022, 10. DOI10.3389/feart.903743. (2022). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 09 Apr, 2026 Reviews received at journal 31 Mar, 2026 Reviewers agreed at journal 25 Mar, 2026 Reviewers agreed at journal 23 Mar, 2026 Reviews received at journal 25 Jan, 2026 Reviewers agreed at journal 22 Jan, 2026 Reviewers invited by journal 15 Oct, 2025 Editor invited by journal 14 Oct, 2025 Editor assigned by journal 11 Oct, 2025 Submission checks completed at journal 11 Oct, 2025 First submitted to journal 04 Oct, 2025 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. 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Right Haunches with Different Interbedding Dip Angles\u003c/p\u003e","description":"","filename":"16.png","url":"https://assets-eu.researchsquare.com/files/rs-7780421/v1/62acfbb3b092e6c67d131552.png"},{"id":94672311,"identity":"559c6216-332c-42fc-9e5f-29fca80cd47c","added_by":"auto","created_at":"2025-10-29 13:40:14","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":321381,"visible":true,"origin":"","legend":"\u003cp\u003eStress Nephograms of Support Forces Under Different Interbedding Dip Angles\u003c/p\u003e","description":"","filename":"17.png","url":"https://assets-eu.researchsquare.com/files/rs-7780421/v1/9c3176360b24872b2de03cf6.png"},{"id":94656640,"identity":"0c5d1b03-7e30-4551-9a90-9efcb2511482","added_by":"auto","created_at":"2025-10-29 10:47:07","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":100398,"visible":true,"origin":"","legend":"\u003cp\u003eStress Nephograms of Support Forces Under Different Interbedding Dip Angles\u003c/p\u003e","description":"","filename":"18.png","url":"https://assets-eu.researchsquare.com/files/rs-7780421/v1/5731aa41114b0c84625acc3e.png"},{"id":94656628,"identity":"b7a9d48a-a91b-49c0-ae16-a28bcc2b290b","added_by":"auto","created_at":"2025-10-29 10:47:06","extension":"png","order_by":19,"title":"Figure 19","display":"","copyAsset":false,"role":"figure","size":820788,"visible":true,"origin":"","legend":"\u003cp\u003eCrack distribution diagrams under different interbedding angles\u003c/p\u003e","description":"","filename":"19.png","url":"https://assets-eu.researchsquare.com/files/rs-7780421/v1/67bdb1a72bb7e92035645ed7.png"},{"id":94728184,"identity":"25bf4905-bd54-4b59-93df-677631ba7d86","added_by":"auto","created_at":"2025-10-30 07:03:17","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":10805197,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7780421/v1/e8dbf340-c270-439b-9727-aaabc2a800c5.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Research on Mechanical Characteristics and Failure Modes of Interbedded Rock Mass with Varying Dip Angles under High In-Situ Stress","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eDue to the complex terrain, hydrogeological conditions, and inherent characteristics of rock formations in western China, tunnel construction in the region is evolving toward greater depth, length, scale, difficulty, and risk\u003csup\u003e\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. During the construction of layered soft rock tunnels in high-altitude areas of western China, engineers face not only challenges such as weak self-stabilization capacity, poor mechanical properties, and water-induced softening of layered rock masses but also multiple stressors including high water pressure, fault-fold structures, and combined tectonic and gravitational stress fields. Consequently, the stress distribution within the surrounding rock-support structure system becomes exceptionally complex, leading to frequent hazards such as support deformation and cracking, extrusion-induced large deformations\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e, high-stress rockbursts\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e, and water inrushes\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. These challenges pose significant difficulties for tunnel design, construction, and subsequent operation and maintenance in western China.Due to the more complex mechanical properties and failure modes of interbedded hard-soft rock masses under varying layer thicknesses and dip angles, the deformation mechanisms of tunnels in such strata under high in-situ stress remain inadequately understood, and deformation control poses greater challenges. This necessitates in-depth systematic investigation\u003csup\u003e\u003cspan additionalcitationids=\"CR11\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eCurrent research on tunnels in stratified rock masses primarily focuses on their physical-mechanical properties, stability, and deformation characteristics. Zhang et al. \u003csup\u003e13\u003c/sup\u003einvestigated the deformation and failure mechanisms of multilayered rock masses using triaxial rheological tests, revealing three dominant failure modes: monoclinic shear failure, tensile crack failure, and interfacial shear-slip failure.Sher\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e employed the three-dimensional boundary element method to determine the stress state of fractured elastic rock masses, establishing the influence of stratified rock strength characteristics on the geometry, dimensions, and area of radial fractures. Crucially, it was demonstrated that fracture morphology can be modified by adjusting the explosive distribution along boreholes.Chekhov \u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003edeveloped an exact analytical approach based on three-dimensional nonlinear theory to investigate surface instabilities in regularly stratified semi-infinite media, providing a rigorous framework for assessing the stability of layered rock formations.Fereshtenejad et al.\u003csup\u003e16\u003c/sup\u003e proposed a practical 3D geometric modeling method for simulating folded rock strata, motivated by the recognition that planar assumptions in prior studies of rocks with curved discontinuities introduce significant errors in subsequent analyses. Their approach utilizes MATLAB scripts to generate optimized input data for mechanical analysis.Triantafyllidis et al.\u003csup\u003e17\u003c/sup\u003e addressed layered rock failure by assuming orthotropic elasticity in components prior to failure. They evaluated local stress-strain states and integrated multiple failure criteria to develop a comprehensive framework encapsulating 3D elasticity and failure mechanisms, validated through case studies elucidating the model's mechanical responses.Berti et al.\u003csup\u003e18\u003c/sup\u003e addressed the challenge of determining physical-mechanical properties in flysch\u0026mdash;a sedimentary rock characterized by soft-hard interbedding. By analyzing large-scale landslides in Cretaceous flysch formations, they compared failure strengths with those predicted using an enhanced Geological Strength Index (GSI) methodology.Bonilla-Sierra et al.\u003csup\u003e19\u003c/sup\u003e integrated photogrammetry and Discrete Fracture Network (DFN)techniques with the Discrete Element Method (DEM). Utilizing the SiroVision 3D mapping system and its structural mapping tools, they imported case-specific geotechnical data of unstable strata into computational models for stability analysis of pre-fractured rock masses.Li et al. \u003csup\u003e20\u003c/sup\u003econducted indoor experiments on soft hard interlayered rock samples in the Jinping area and analyzed three failure modes caused by different distribution forms of weak layers under uniaxial compression, as well as the deformation and failure characteristics of rock samples under different loading paths under biaxial compression. They further studied the influence of the dip angle, quantity, distribution form, and volume ratio of weak layers on the strength characteristics.\u003c/p\u003e\u003cp\u003eStudies by the aforementioned experts indicate that research on the mechanical properties and failure modes of layered rock masses has primarily focused on analyzing physical-mechanical characteristics and failure patterns through laboratory experiments considering different rock mass properties. However, integrated approaches combining laboratory testing with discrete element analysis remain scarce. Therefore, this study conducts laboratory experiments to analyze the mechanical behavior and failure mechanisms of interbedded rock masses at varying dip angles, and employs discrete element modeling (DEM) to comparatively investigate surrounding rock displacement, support loading, and crack propagation in tunnels constructed within such strata. This integrated methodology aims to offer insights for the construction and support design of interbedded rock tunnels under high in-situ stress conditions.\u003c/p\u003e"},{"header":"2. Engineering Overview","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Engineering background\u003c/h2\u003e\u003cp\u003eThe Yinlan High-speed Railway Zhonglan section spans a total length of 219.671 km, with newly constructed double-track tunnels measuring 50.626 km across 25 tunnels, accounting for 23.0% of the total route length. Among these, the Xiangshan Tunnel and Jianshan Tunnel are key projects of the entire line.\u003c/p\u003e\u003cp\u003eThe Jianshan Tunnel extends from chainage DK109\u0026thinsp;+\u0026thinsp;780 to DK115\u0026thinsp;+\u0026thinsp;782, with a total length of 6,002 m. It is the longest tunnel on the Zhonglan Passenger Dedicated Line (Gansu Section) and the only water-abundant tunnel along the entire route. The design elevation of the tunnel entrance shoulder is 1,356.34 m, while the exit shoulder elevation is 1,640.08 m, featuring a unidirectional longitudinal grade.\u003c/p\u003e\u003cp\u003eThe entrance construction section spans 2,075 m with a maximum burial depth of 519 m. The tunnel body traverses 7 fault zones, posing risks of sudden collapse and presenting extremely high construction challenges and safety risks.\u003c/p\u003e\u003cp\u003eThe lithology of the strata in this area is relatively complex, dominated primarily by sedimentary and metamorphic rocks, with exposed formations comprising Quaternary unconsolidated deposits; Jurassic Middle Series Honggou Formation sandstone interbedded with mudstone; Devonian Lower-Middle Series Xueshan Group sandstone interbedded with conglomerate; Silurian Lower Series Magouying Formation metamorphic sandstone interbedded with phyllite; and alternating beds of metamorphic sandstone and mudstone within the Silurian Lower Series Magouying Formation, all of which consist of unweathered rock.\u003c/p\u003e\u003cp\u003eThe rock strata exhibit steep inclination, with their strike essentially parallel to the tunnel axis. The surrounding rock conditions at the tunnel face are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Analysis of In-situ Stress Measurement Results\u003c/h2\u003e\u003cp\u003eConsidering comprehensive factors including on-site engineering geological conditions, specialized testing agencies were collaboratively engaged to conduct two separate hydraulic fracturing stress measurements at specific locations within the Jianshan Tunnel during distinct time periods (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eA borehole was drilled at chainage DK113\u0026thinsp;+\u0026thinsp;710 near the tunnel axis elevation for the initial stress measurement. As per engineering design specifications, the planned final borehole depth was 274.91 m. However, during testing operations, severe borehole wall collapse and rock fragmentation occurred, limiting instrument penetration to approximately 163 m. Through technical coordination, stress measurements were successfully conducted in the accessible section above the obstruction point (~\u0026thinsp;163 m).\u003c/p\u003e\u003cp\u003eWithin the 99\u0026ndash;163 m depth interval, data from 12 measurement segments were successfully acquired, with 8 segments yielding well-defined maximum and minimum horizontal principal stress values. Using fracturing parameters - including breakdown pressure reopening pressure, and instantaneous shut-in pressure - the maximum (SH) and minimum (Sh) horizontal principal stresses were calculated. The computational results, along with vertical stress (Sv) values, are detailed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eIn-situ Stress Measurement Results Table for Borehole D2Z-Jian-15, Jianshan Tunnel.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"12\"\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\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" 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rowspan=\"2\"\u003e\u003cp\u003eNo.\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eInterval Depth(m)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003eFracturing Parameters (MPa)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c10\" namest=\"c7\"\u003e\u003cp\u003ePrincipal Stresses (MPa)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c11\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003e\u003cem\u003eλ\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c12\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eσ\u003csub\u003eH\u003c/sub\u003eOrientation (\u0026deg;)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" 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align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1.71\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e3.62\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e2.79\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e2.91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e1.24\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e117.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e3.32\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.72\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1.59\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e3.27\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e2.77\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e3.16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e1.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e126.48\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e4.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1.92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e3.84\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e3.19\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e3.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e1.12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e131.18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e4.19\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.58\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2.12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.62\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e4.13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e3.43\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e3.54\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e1.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003eN12\u0026deg;E\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e141.65\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e3.71\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.72\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1.92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e4.47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e3.33\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e3.82\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e1.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e150.86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e4.93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e3.70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.48\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e1.23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e4.27\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e3.65\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e4.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e1.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003eN23\u0026deg;E\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e155.46\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e5.12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e4.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2.39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e4.45\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e3.94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e4.20\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e\u003cp\u003e1.06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\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\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e-In-situ rock fracture initiation pressure;\u003cem\u003ePr\u003c/em\u003e-Fracture reopening pressure༛\u003cem\u003ePs\u003c/em\u003e-Fracture closure pressure༛\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e-Formation pore pressure at measurement depth༛\u003cem\u003eT\u003c/em\u003e-Rock tensile strength༛\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e-Aximum horizontal principal stress; \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e-Minimum horizontal principal stress༛\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003eV\u003c/em\u003e\u003c/sub\u003e-Overburden stress (calculated with rock density 2700 kg/m\u0026sup3;).\u003c/p\u003e\u003cp\u003eAs evidenced in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the magnitude relationship among the three principal stresses exhibits \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e \u0026gt;\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003eV\u003c/em\u003e\u003c/sub\u003e \u0026gt;\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e.The maximum horizontal principal stress exceeding the vertical stress indicates a predominantly horizontal stress regime in the vicinity of the borehole.\u003c/p\u003e\u003cp\u003eThe lateral pressure coefficient (\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e /\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003eV\u003c/em\u003e\u003c/sub\u003e) ranges from 1.03 to 1.24, with a mean value of 1.14. This is significantly higher than the lithostatic pressure coefficient (generated solely by overburden weight)\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003e, demonstrating that the in-situ stress field within the measurement depth is subject to the collective influence of tectonic stresses and topographic valley effects.\u003c/p\u003e\u003cp\u003eThe hydraulic fracturing stress measurement results indicate that:The in-situ stress field in the Jianshan Tunnel area is primarily controlled by tectonic stresses;The surrounding stress regime exhibits NE-oriented compressive stresses; Horizontal stresses dominate throughout the region.\u003c/p\u003e\u003cp\u003eFor the second test, hydraulic fracturing was again employed to conduct in-situ stress measurements in the Jianshan Tunnel. The selected test location was at chainage DK113\u0026thinsp;+\u0026thinsp;400, with the borehole collar approximately 310 m below ground surface and a drilling depth of 35.2 m.\u003c/p\u003e\u003cp\u003eBased on initial data including geological conditions, Rock Quality Designation (RQD) of core samples, and borehole sediment, bottom-up stress testing was conducted at three intervals. However, only two sets of reliable data were obtained from measurement depths of 28.43 m and 32.57 m.The pressure recording curves for the measurement intervals are presented in Fig.\u0026nbsp;3.\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\u003eCharacterization Parameters of Fracturing and Calculated In-situ Stresses.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"11\"\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\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eNo.\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eInterval Depth(m)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u003cp\u003eFracturing Parameters (MPa)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c10\" namest=\"c7\"\u003e\u003cp\u003ePrincipal Stresses (MPa)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c11\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003e\u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003eOrientation (\u0026deg;)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cem\u003eT\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c9\"\u003e\u003cp\u003e\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c10\"\u003e\u003cp\u003e\u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003ev\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e28.43\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e9.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e8.86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e6.49\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e10.89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e6.77\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e8.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003eN40.6\u0026deg;E\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e32.57\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e7.90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e7.64\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e6.57\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.33\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e12.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e6.90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e9.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003eN27.3\u0026deg;E\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\u003eAccording to the Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e2\u003c/span\u003e, at a depth of 342.57 m:Maximum horizontal stress comes to 12.40 MPa;Saturated uniaxial compressive strength \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e\u0026lt;30 MPa (classified as soft rock).When \u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003e= 2\u0026ndash;4 ,belong to high in-situ stress conditions;When \u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003e\u0026lt;\u0026thinsp;2, belong to extremely high in-situ stress conditions.Therefore, there is high ground stress at the deeper part of the Jianshan Tunnel, and the possibility of rock burst during construction is low. There is a possibility of soft rock deformation and damage, mainly due to accidents such as roof caving.\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Study on Mechanical Properties of Interbedded Rock Masses","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Sampling of Interbedded Rock Masses\u003c/h2\u003e\u003cp\u003eTo analyze the fundamental characteristics of in-situ interbedded rock samples, core sampling was conducted at the high-stress section DK112\u0026thinsp;+\u0026thinsp;160, based on:Geological reconnaissance within the tunnel zone and In-situ stress measurements from Jianshan Tunnel.\u003c/p\u003e\u003cp\u003eThe sampled lithology primarily consists of sandstone-mudstone interbeds. Specimens were extracted through precision coring for laboratory testing under multiaxial stress conditions (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTo investigate the compression failure modes of soft-hard interbedded rock masses under different bedding dip angles, five groups of standard cylindrical specimens (50 mm in diameter and 100 mm in height) were prepared at varying dip angles. Each group contained no fewer than four specimens with dip angles of 0\u0026deg;, 30\u0026deg;, 45\u0026deg;, 60\u0026deg;, and 90\u0026deg; respectively. The sampling method is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e, while specimens with different dip angles are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The sandstone layers (primarily 1\u0026ndash;2 cm thick) exhibited relatively high strength, whereas the mudstone layers (mainly 0.5-1 cm thick) showed lower strength. All specimens exhibited distinct interbedding features.\u003c/p\u003e\u003cp\u003eThe prepared specimens were systematically numbered according to their dip angles to facilitate subsequent data recording during uniaxial and triaxial compression tests, as well as for post-failure pattern observation (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe numbered specimens were subjected to uniaxial and triaxial compression tests using a YAW-2000M multifunctional rock testing system (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e) in the rock mechanics laboratory. This apparatus features high stability and precise control accuracy.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Analysis of Uniaxial Compression Results for Interbedded Rock\u003c/h2\u003e\u003cp\u003eThe uniaxial compression test results for interbedded rock specimens with varying dip angles are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFrom Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e, it can be seen that the stress-strain curves of specimens with different angles of soft and hard interlayers mainly consist of five stages: 1) primary compaction stage: in this stage, the stress-strain curve shows a slightly upward bending trend, and there are basically no cracks appearing on the surface of the rock mass; 2) Elastic development stage: In this stage, the stress-strain curve shows an oblique linear rise, accompanied by a continuous increase in load. Cracks have already appeared inside the rock, and there are also subtle cracks on the surface. In this stage, the cracks are not obvious but have already appeared and continued to develop (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e (a)); 3) Strain hardening stage: During this stage, the stress-strain curve shows a significant nonlinear change, and the number of cracks increases significantly, mainly shear cracks accompanied by the appearance of tensile cracks (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e (b)); 4) Strain softening stage: After the uniaxial compressive bearing capacity reaches its peak, the actual internal structure of the component has been destroyed, and most of the specimens can still maintain a basic stable shape. The stress decay rate is very fast, and the crack development rate increases, rapidly expanding and connecting into a fracture surface (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e (c)); 5) Post peak residual stage: In this stage, the stress-strain curve of the specimen shows a significant and rapid decrease due to its failure, basically dropping to 0. Macroscopically, it is manifested as block slip of the rock mass (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e (d)).\u003c/p\u003e\u003cp\u003eFrom Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e, it is also found that the stress-strain curves of different inclination angles show brittle failure. At lower inclination angles (0 \u0026deg;~30 \u0026deg;), the strain corresponding to the peak strength of the specimen is usually between 0.4% and 0.5%; When the inclination angle is moderate (45 \u0026deg;~60 \u0026deg;), the strain corresponding to the peak strength of the specimen is usually between 0.2% and 0.3%; When the inclination angle is large (90 \u0026deg;), the strain corresponding to the peak strength of the specimen is usually between 0.5% and 0.6%. That is to say, the strain required for the specimen to reach the peak strength at a medium inclination angle is smaller, resulting in faster structural failure. In addition, during the process of the inclination angle from 0 \u0026deg; to 60 \u0026deg;, the peak uniaxial compressive strength decreases continuously. When the inclination angle is 0 \u0026deg;, the compressive strength is 14.28 MPa; When the inclination angle is 30 \u0026deg;, the compressive strength is 11.65 MPa, with a decrease of 18.42%; When the inclination angle is 45 \u0026deg;, the compressive strength is 7.3 MPa, with a decrease of 48.88%; When the inclination angle is 60 \u0026deg;, the compressive strength is 4.6 MPa, with a decrease of 67.79%. When the inclination angle changes from 60 \u0026deg; to 90 \u0026deg;, the uniaxial compressive strength increases to 14.02 MPa, slightly lower than the compressive strength at 0 \u0026deg;. From the above data, it is not difficult to see that the layered rock mass has obvious anisotropy.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFurther analysis reveals that:At low dip angles (0\u0026deg;\u0026ndash;30\u0026deg;), the axial strain tends to be relatively large, and a certain amount of strain persists even in the post-peak residual stage. In interbedded rock masses, the soft layers typically exhibit low elastic modulus and overall lower strength, indicating that the mechanical behavior of the interbedded rock is primarily governed by the soft layersin this range.At medium dip angles (45\u0026deg;-60\u0026deg;), failure of the interbedded rock mass mainly manifests as sliding failure, predominantly along the interfaces between soft and hard layers. This suggests that the mechanical properties are dominated by the soft-hard interlayer interfaces in this range.At high dip angles (90\u0026deg;), the load is jointly borne by both the soft and hard layers. However, due to the higher strength of the hard layers, the mechanical behavior of the interbedded rock mass is predominantly controlled by the hard layers in this case.Even after the axial stress drops in the post-peak residual stage, a certain residual strength is retained. This is because: Crack propagation may exhibit nonlinear characteristics, meaning the rock mass is not entirely destroyed internally.Alternatively, complete failure may be confined to a specific layer (often the soft layer), while the specimen as a whole remains partially intact, allowing it to retain some load-bearing capacity.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Analysis of Triaxial Compression Results for Interbedded Rock Mass\u003c/h2\u003e\u003cp\u003eBased on in-situ stress measurements, the confining pressures in this triaxial test were set at 5 MPa, 10 MPa, and 15 MPa. The stress-strain relationship curves under varying confining pressures and dip angles during the test are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFrom Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e(a), it can be observed that in triaxial tests under 5 MPa confining pressure, specimens with different dip angles exhibit varying post-peak residual strengths after reaching peak strength. Specifically, specimens with small dip angles (0\u0026deg;, 30\u0026deg;) and large dip angles (90\u0026deg;) show higher post-peak residual strengths, whereas those with medium dip angles (45\u0026deg;, 60\u0026deg;) exhibit lower post-peak residual strengths.\u003c/p\u003e\u003cp\u003eIn the later stage of strain, the rock mass demonstrates certain ductile characteristics at small and large dip angles, while at medium dip angles, it displays some brittle features. Overall, under confining pressure, the stress-strain behavior of interbedded rock specimens varies to some extent depending on the dip angle..\u003c/p\u003e\u003cp\u003eA comparison of the three diagrams in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e reveals that under low confining pressure, the stress of the interbedded rock mass drops rapidly after reaching peak strength, exhibiting significant softening characteristics. When the confining pressure is increased, the post-peak stress decreases more gradually with increasing strain, and the strain softening phenomenon progressively weakens. In the later stage of strain, the interbedded rock mass demonstrates ductile failure characteristics.\u003c/p\u003e\u003cp\u003eFurthermore, by comparing the stress-strain curves of specimens with the same interbedding dip angle under different confining pressures, it can be observed that high confining pressure promotes a transition from brittle to ductile behavior in both small-dip and large-dip rock masses. However, this change is not particularly pronounced in interbedded rock specimens with medium dip angles.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e3.4 Analysis of Failure Modes in Uniaxial Compression of Interbedded Rock Masses\u003c/h2\u003e\u003cp\u003eThe stability of rock is closely related to the distribution and propagation of cracks on its surface and within its internal structure. Typically, rock instability is caused by crack propagation and the interconnection of different cracks. Studying the failure modes of interbedded specimens under compression helps to fundamentally clarify the failure mechanisms of interbedded rock.\u003c/p\u003e\u003cp\u003eDuring uniaxial compression tests, audible cracking sounds were observed in interbedded specimens of all dip angles upon failure, and their stress-strain curves exhibited distinct brittle characteristics. The failure patterns are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eThe location and propagation pattern of cracks play a decisive role in the ultimate failure mode of rock masses. As can be observed from Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003e:\u003c/p\u003e\u003cp\u003eFor specimens with small dip angles (predominantly 0\u0026deg;, with a few at 30\u0026deg;), due to their high peak strength and elastic modulus, cracks find it difficult to propagate in the soft-hard interbedded rock mass because the soft layers exhibit certain ductility. Consequently, failure typically initiates in the hard layers and gradually extends to the soft layers, ultimately forming vertical fissures that penetrate both the soft and hard strata.\u003c/p\u003e\u003cp\u003eAdditionally, due to the deformation incompatibility between the soft and hard layers, the soft layers may undergo compressive deformation first, generating transverse forces at their interfaces. Under these transverse forces, tensile cracks perpendicular to the force direction develop and propagate in the interbedded rock mass. The resulting cracks are vertical tensile cracks that penetrate the entire soft-hard bedding planes (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003e(a)), characteristic of splitting failure.\u003c/p\u003e\u003cp\u003eThe moderately inclined rock specimens (mainly at 45\u0026deg;, with some at 60\u0026deg;) exhibit relatively low peak strength and elastic modulus. During compression, the interbedded specimens with moderate inclination experience some slippage between the soft and hard layers. Due to the larger inclination angle of these moderately interbedded specimens, the slippage phenomenon is more pronounced. When the interface between the soft and hard interbeds can no longer withstand the shear stress, sliding failure occurs. At this stage, the oblique cracks are predominantly shear cracks, with fewer tensile cracks. The cracks generated in the rock mass are oblique cracks that penetrate the entire soft-hard bedding plane (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003e(b)), indicating a shear failure mode.\u003c/p\u003e\u003cp\u003eHigh-angle rock specimens (predominantly 90\u0026deg;, with a few at 60\u0026deg;) exhibit a combined failure mode due to the simultaneous compression of both soft and hard layers. However, the difference in their elastic moduli leads to uneven deformation rates, promoting crack propagation and the formation of fracture surfaces. Under the combined action of tensile stress and shear stress, the cracks develop into vertical tensile fractures and inclined shear cracks.\u003c/p\u003e\u003cp\u003eThe resulting fractures in the rock mass represent a composite failure mode, combining tensile splitting (cleavage) and shear slippage (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003e(c)), thus classifying it as a mixed failure mechanism.\u003c/p\u003e\u003cp\u003eUnder uniaxial compression, interbedded rock specimens with varying dip angles exhibit three primary failure modes: splitting (tensile) failure, shear failure, and composite failure. Observations of the failure patterns reveal that in interbedded rock masses, the soft layers, due to their higher ductility, tend to inhibit crack propagation, resulting in slower fracture development. This suggests that increasing the thickness of soft layers in soft-hard interbedded rock masses can, to some extent, suppress crack coalescence and the formation of macroscopic fracture surfaces, thereby enhancing the overall stability of the rock mass.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e3.5 Analysis of Triaxial Compression Failure Modes in Interbedded Rock Masses\u003c/h2\u003e\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eUnder triaxial compression tests, the ultimate failure modes of soft-hard interbedded rock masses with different dip angles are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003e. In addition to the influence of dip angles, the application of varying confining pressures leads to distinct characteristics in the failure patterns, crack propagation trends, and coalescence forms of the interbedded rock masses.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eAs can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003e, there are certain differences in the failure modes of soft-hard interbedded rock specimens with different dip angles under varying confining pressures. Under triaxial compression, as the confining pressure increases, shear failure becomes more prevalent in the rock mass.\u003c/p\u003e\u003cp\u003eAdditionally, due to the distinct physical and mechanical properties of soft and hard layers, the constraining effect of confining pressure on the expansive deformation of soft layers is significantly weaker than that on hard layers. This leads to deformation incompatibility between soft and hard layers under confining pressure. Coupled with the cohesive forces between the layers, the soft layers, which undergo greater expansion, experience volumetric swelling. As a result, misaligned sliding occurs between the soft and hard interbeds, leading to shear failure in the interbedded rock specimens.\u003c/p\u003e\u003cp\u003eTherefore, under low confining pressure:\u003c/p\u003e\u003cp\u003eFor small-dip-angle interbedded specimens, the failure mode primarily involves tensile cracks localized in the hard layers, with overall splitting failure dominating. Vertical cracks appear on the specimen surface, and while the failure is incomplete, the specimen retains some integrity (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003e(a)).\u003c/p\u003e\u003cp\u003eFor medium-dip-angle specimens, localized tensile cracks occur, along with inclined cracks penetrating the entire specimen. Shear failure dominates, and the destruction is more thorough (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003e(b)).\u003c/p\u003e\u003cp\u003eFor large-dip-angle specimens, the failure mode features inclined cracks running through the entire rock mass, primarily exhibiting shear failure. The destruction is relatively thorough, though the failure location differs somewhat from that of medium-dip-angle specimens (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003e(c)).\u003c/p\u003e\u003cp\u003eWhen the confining pressure increases, the soft-hard interbedded rock specimens with different dip angles are more prone to shear failure. At this point, regardless of whether the specimens have a small, medium, or large dip angle, inclined cracks are observed.\u003c/p\u003e\u003cp\u003eUnder high confining pressure, small-dip-angle interbedded specimens exhibit longitudinal, slightly inclined cracks penetrating the entire sample. These cracks consist of a main fracture and several minor cracks. The primary failure mode is splitting failure, with minimal overall fragmentation, allowing the specimen to maintain its integrity.\u003c/p\u003e\u003cp\u003eFor medium-dip-angle interbedded specimens, the dominant failure mode includes inclined cracks traversing the entire specimen, along with a few vertical and horizontal cracks. The failure is mainly a combination of shear and splitting failure. The inclined cracks propagate rapidly, forming large, continuous fracture surfaces. During failure, rock debris is generated, leading to severe damage and a loss of self-stability.\u003c/p\u003e\u003cp\u003eIn large-dip-angle specimens, the failure primarily manifests as localized inclined cracks, with crack size and propagation speed decreasing as confining pressure increases. The dominant failure mode is shear failure, producing wide cracks that do not fully connect into a continuous fracture surface. As a result, the rock mass retains its self-stability.\u003c/p\u003e\u003cp\u003eFrom the triaxial test results, unlike uniaxial compression tests, although the soft layers in soft-hard interbedded rock masses still inhibit crack propagation, this inhibitory effect does not increase linearly. When the thickness of the soft layers varies within a certain range, their influence on crack extension is most pronounced. If the soft layer thickness falls outside this range, two scenarios may occur:\u003c/p\u003e\u003cp\u003e① When the soft layer thickness exceeds this range, the skeletal structural effect formed by the inherent physical and mechanical properties of the hard layers diminishes. Additionally, due to the larger thickness of the soft layers, the spacing between hard layers increases, weakening stress transfer. As a result, the proportion of stress borne by the hard layers decreases, while the soft layers bear higher stress. However, under triaxial conditions, the confining pressure restricts the expansive deformation of the soft layers, preventing stress release and leading to crack initiation.\u003c/p\u003e\u003cp\u003e② When the soft layer thickness is below this range, the thin soft layers fail to provide sufficient stress buffering, reducing the overall stability of the rock strata. Consequently, cracks interconnect and coalesce, forming fractures.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Deformation Characteristics of Interbedded Tunnels Based on Discrete Element Analysis","content":"\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003e4.1 Overview\u003c/h2\u003e\u003cp\u003ePrevious studies investigated the mechanical properties and failure modes of interbedded rock masses under uniaxial and triaxial compression through laboratory tests. However, as a complex geological material, rock inherently contains numerous defects. With the increase in scale of rock engineering, research focus has gradually shifted from intact rock to jointed and fractured rock masses. In practical engineering, evaluating the mechanical stability of rock masses and the structural safety of tunnels requires analysis of rock strength, deformation and failure characteristics, as well as crack propagation behavior.\u003c/p\u003e\u003cp\u003eRock masses are often intersected by multiple joints or structural planes, making them unsuitable for treatment as continuous media in certain cases. Due to their pronounced discontinuities, conventional continuum mechanics methods (such as the finite element method) may prove inadequate. In such scenarios, the discrete element method (DEM) offers a more rational approach for analyzing discontinuous media, particularly for jointed rock masses.\u003c/p\u003e\u003cp\u003e3DEC (3 Dimension Distinct Element Code) is the abbreviation for a three-dimensional discrete element method program. Building upon the core principles of UDEC, it extends the two-dimensional planar discrete medium mechanics into three-dimensional space.\u003c/p\u003e\u003cp\u003eAs a program based on the discrete element method (DEM), 3DEC describes the mechanical behavior of discontinuous media. It adopts the same finite difference approach as FLAC while incorporating simulations of discontinuous behavior at contact interfaces in terms of mechanics.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003e4.2 Model Establishment and Parameter Selection\u003c/h2\u003e\u003cp\u003eThe following assumptions were adopted in the numerical modeling and analysis of this study:\u003c/p\u003e\u003cp\u003e(1) The surrounding rock contains only joints with a single orientation and uniform mechanical properties;\u003c/p\u003e\u003cp\u003e(2) In the computational model, the constitutive models for blocks and joint elements are transversely isotropic and zone-contact elastoplastic (based on Coulomb slip failure), respectively;\u003c/p\u003e\u003cp\u003e(3) The influences of groundwater and temperature fields are not considered;\u003c/p\u003e\u003cp\u003e(4) Secondary lining structures are excluded from the calculation process as a safety reserve.\u003c/p\u003e\u003cp\u003eThe discrete element model was established using 3DEC 7.0 software. Based on the results of discrete element numerical analyses from relevant previous literature and engineering accuracy requirements[21\u0026ndash;22], while balancing computational efficiency and result precision, the overall model dimensions were ultimately determined as 100m (length) \u0026times; 100m (width) \u0026times; 30m (height). The upper surface was defined as a free boundary, with displacement constraints applied to all other surfaces. Boundary forces were applied according to in-situ stress measurement results from the tunnel site.\u003c/p\u003e\u003cp\u003eTo address computational challenges associated with the discrete element method (including large calculation volumes, numerous elements, and time-consuming processes), the model was appropriately simplified based on field geological investigations. The central 50m \u0026times; 50m area of the model was designated as interbedded hard rock (sandstone) and soft rock (mudstone), while surrounding regions were modeled as homogeneous, non-interbedded Grade V rock mass.\u003c/p\u003e\u003cp\u003eMultiple discrete element models were developed within the central zone with varying hard/soft layer thickness ratios and dip angles. Tunnel excavation was simulated using the three-bench method, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e12\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe mechanical parameters adopted for the layered rock mass in this study are presented in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e2\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 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eRock Mechanics Parameters.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\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\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRock Mas\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eUnit Weight\u003c/p\u003e\u003cp\u003e\u003cem\u003eγ\u003c/em\u003e /kN.m\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eElastic Modulus\u003c/p\u003e\u003cp\u003e\u003cem\u003eE\u003c/em\u003e /GPa\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003ePoisson's Ratio\u003cem\u003e\u0026micro;\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eInternal Friction Angle\u003c/p\u003e\u003cp\u003e\u003cem\u003eϕ\u003c/em\u003e/。\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eCohesion\u003c/p\u003e\u003cp\u003e\u003cem\u003ec\u003c/em\u003e /MPa\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHard Rock\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2250\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e5.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e36\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e12.0\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSoft Rock\u003c/p\u003e\u003cp\u003eGrade V Surrounding Rock\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2000\u003c/p\u003e\u003cp\u003e1800\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.30\u003c/p\u003e\u003cp\u003e1.50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.35\u003c/p\u003e\u003cp\u003e0.39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e15\u003c/p\u003e\u003cp\u003e22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003cp\u003e0.12\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe shotcrete employs C25-grade concrete, with steel frames consisting of I20-section steel members. The mechanical parameters of the primary support and steel frames are detailed in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePrimary Support Parameters Table.\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=\"left\" 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=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMaterial Type\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eThickness\u003c/p\u003e\u003cp\u003e\u003cem\u003ed\u003c/em\u003e/cm\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eElastic Modulus\u003c/p\u003e\u003cp\u003e\u003cem\u003eE\u003c/em\u003e/GPa\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eUnit Weight\u003c/p\u003e\u003cp\u003e\u003cem\u003eγ\u003c/em\u003e/kN.m\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003ePoisson's Ratio\u003cem\u003e\u0026micro;\u003c/em\u003e\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC25 Shotcrete\u0026thinsp;+\u0026thinsp;Steel Frame\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e25.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2400\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\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\u003cp\u003eΦ22 rock bolts are employed, with detailed specifications provided in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e4\u003c/span\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 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eAnchor Bolt Parameters.\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=\"left\" 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=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLength/m\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eArea\u003c/p\u003e\u003cp\u003eA/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eElastic Modulus\u003c/p\u003e\u003cp\u003eE/GPa\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eGrout Stiffness\u003c/p\u003e\u003cp\u003ek/GPa\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eBond Strength\u003c/p\u003e\u003cp\u003es/MPa\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3.8e-4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e200\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e8.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e6.91\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\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003e4.3 Discrete Element Result Analysis\u003c/h2\u003e\u003cp\u003e(1) Surrounding Rock Displacement\u003c/p\u003e\u003cp\u003eModels were established with a hard rock to soft rock thickness ratio of 1:1,The reason for selecting a 1:1 thickness ratio in the model and its rationale, within the proportion range of soft-to-hard interbedded rock layers measured by field sampling. The dip angles selected for analysis correspond to those used in laboratory tests, namely 0\u0026deg;, 30\u0026deg;, 45\u0026deg;, 60\u0026deg;, and 90\u0026deg;. The numerical models for each case are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e13\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe displacement nephograms under high in-situ stress conditions for varying interbedded dip angles are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e14\u003c/span\u003e (using 0\u0026deg; and 60\u0026deg; cases as representative examples).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e15\u003c/span\u003e:\u003c/p\u003e\u003cp\u003eWhen the bedding planes of the interbedded rock mass are horizontal, the vault settlement reaches its maximum value of 268.84 mm. The softening effect of soft layers results in a lower deformation modulus of the soft-hard interbedded rock mass. With horizontal bedding, the tensile-bending resistance at the vault is relatively weak. Under significant overburden depth, the self-weight of the overlying rock mass tends to cause unilateral flexural failure, leading to substantial vertical deformation in the surrounding rock.\u003c/p\u003e\u003cp\u003eThe vault settlement exhibits a decreasing trend within the 0\u0026deg;\u0026ndash;45\u0026deg; inclination range but increases within the 45\u0026deg;\u0026ndash;90\u0026deg; range. This indicates that as the interbedded rock transitions from low to medium dip angles, the increase in inclination reduces tensile-bending effects, resulting in relatively smaller vault displacement. However, when the rock mass shifts from medium to high dip angles, bedding-plane slip drives continuous displacement growth. At medium dip angles, the mechanical behavior of the interbedded rock becomes more complex, potentially involving simultaneous tensile-bending and bedding-plane slip\u0026mdash;a finding consistent with laboratory test results.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eDue to the effect of high in-situ stress, the maximum horizontal displacement of the surrounding rock is significantly greater than the vertical displacement. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e16\u003c/span\u003e:\u003c/p\u003e\u003cp\u003eAs the dip angle of interbedded layers increases, the displacement at the left haunch first decreases and then increases. The inclination of rock layers not only causes the left surrounding rock to tend to slide away from the free surface, but also induces mutual compression between rock masses, potentially leading to stress concentration.\u003c/p\u003e\u003cp\u003eConversely, the displacement at the right haunch initially increases slowly and then decreases with increasing dip angle. Larger dip angles amplify bedding-plane slip in the surrounding rock. Additionally, given the lower tensile and shear strength of soft rock layers, plastic flow becomes more likely at steeper angles, resulting in extrusion displacement.\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e16\u003c/span\u003e categorizes the asymmetric deformation of interbedded rock masses under high in-situ stress into four distinct zones based on displacement disparities between left and right haunches:Slow Progression Zone of Asymmetric Deformation;Rapid Development Zone of Asymmetric Deformation;Stabilization Zone of Asymmetric Deformation;Mitigation Zone of Asymmetric Deformation\u003c/p\u003e\u003cp\u003e0\u0026deg;\u0026ndash;30\u0026deg; dip range:\u003c/p\u003e\u003cp\u003eAsymmetric deformation initiates from symmetrical displacement (observed at 0\u0026deg; horizontal bedding). This phase exhibits gradual asymmetric progression with emerging yet limited displacement differences between left and right haunches.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003e30°–45° dip range:\u003c/h3\u003e\n\u003cp\u003eAsymmetric deformation undergoes accelerated development, peaking at 45\u0026deg; where the displacement disparity reaches its maximum.\u003c/p\u003e\n\u003ch3\u003e45°–60° dip range:\u003c/h3\u003e\n\u003cp\u003ePost-peak asymmetric deformation shows slight decline at a subdued rate, maintaining overall stability within a defined range. At 60\u0026deg;, significant displacement differences persist between both haunches.\u003c/p\u003e\n\u003ch3\u003e60°–90° dip range:\u003c/h3\u003e\n\u003cp\u003eA pronounced mitigation trend emerges in asymmetric deformation. By 90\u0026deg; (vertical bedding), haunch displacements become nearly symmetrical\u0026mdash;exhibiting negligible difference similar to the 0\u0026deg; horizontal condition.\u003c/p\u003e\u003cp\u003e(2) Support Forces\u003c/p\u003e\u003cp\u003eThe stress nephograms of the primary support structure under different dip angles are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e17\u003c/span\u003e, with 30\u0026deg; and 45\u0026deg; taken as examples here.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAs can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e17\u003c/span\u003e, when the interbedding dip angle is 30\u0026deg;, the support structure is subjected to a maximum tensile stress of 2.33 MPa and a maximum compressive stress of 18.32 MPa; at a dip angle of 45\u0026deg;, the maximum tensile stress is 1.65 MPa, and the maximum compressive stress reaches 20.72 MPa.\u003c/p\u003e\u003cp\u003eTo more intuitively analyze the support forces at different locations of the tunnel under varying interbedding dip angles, the numerical simulation results at each point were extracted and summarized, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e18\u003c/span\u003e below.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFrom Fig.\u0026nbsp;\u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e18\u003c/span\u003e, the following observations can be made:\u003c/p\u003e\u003cp\u003e① Regarding the maximum principal stress of the supporting structure, the stress at the vault reaches 2.57 MPa at 0\u0026deg;. The stress at the vault varies only slightly with the inclination angle, showing an initial decrease followed by an increase.\u003c/p\u003e\u003cp\u003e② For the left and right arch shoulders and the left and right arch haunches of the supporting structure, the stress fluctuates significantly with the inclination angle. The maximum tensile stress difference occurs at the arch shoulders between 45\u0026deg; and 60\u0026deg;. However, since the overall tensile stress values are relatively small, this region is classified as a minor eccentric tension zone.\u003c/p\u003e\u003cp\u003e③ The stresses at the left and right arch haunches follow a similar trend with changing inclination angles, but the maximum compressive stress difference occurs within the 30\u0026deg;\u0026ndash;60\u0026deg; range. This area covers a wide range with a substantial stress difference, making it a major eccentric compression zone.\u003c/p\u003e\u003cp\u003e④ The stresses at the left and right arch shoulders and the left and right arch haunches also exhibit asymmetry. The maximum stress differences reach 0.43 MPa and \u0026minus;\u0026thinsp;1.21 MPa, respectively, indicating that in interbedded hard and soft strata, medium inclination angles lead to a stress state dominated by eccentric compression with supplementary eccentric tension.\u003c/p\u003e\u003cp\u003e⑤ The stresses at the vault and right arch haunch are the highest, bearing greater surrounding rock pressure. Therefore, during construction, in addition to pre-reinforcement in high-stress areas, the timing of support installation must be carefully controlled to prevent excessive pressure on the supporting structure, which could lead to damage.\u003c/p\u003e\u003cp\u003e(3) Crack Propagation Analysis\u003c/p\u003e\u003cp\u003eAs previously discussed, for tunnels in high-stress interbedded soft and hard rock strata, crack development is a critical factor affecting subsequent surrounding rock stability. Crack propagation typically undergoes three stages: nucleation, steady-state growth, and unstable growth. Once cracks enter the unstable propagation stage, irreversible damage occurs to the material, posing significant hazards.\u003c/p\u003e\u003cp\u003eCurrently, for interbedded soft rock under high stress, most studies rely on finite element analysis, leaving limited research on crack behavior. However, the 3DEC discrete element software can analyze crack distribution and evolution by examining joint opening displacements. Therefore, this section investigates crack distribution under different interbedding angles with equal layer thickness, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e19\u003c/span\u003e (using 45\u0026deg; and 90\u0026deg; as examples).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAs can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e19\u003c/span\u003e: Based on a joint opening displacement of 3 mm, the crack distribution under different interbedding dip angles is closely related to the dip angle, with cracks generally propagating parallel to the bedding plane.\u003c/p\u003e\u003cp\u003eAt a 90\u0026deg; dip angle, all cracks propagate downward, primarily concentrated in the left and right arch shoulders and arch haunches. The maximum crack width reaches 28.11 mm, occurring at the right arch foot.\u003c/p\u003e\u003cp\u003eAt a 45\u0026deg; dip angle, cracks predominantly follow a 45\u0026deg; trajectory, mainly distributed at the right arch shoulder and the left arch haunch and waist. The maximum crack width reaches 71.65 mm, and the number of cracks is significantly higher than that at the 90\u0026deg; dip angle.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003e\u003cb\u003e.\u003c/b\u003eMaximum crack length at different dip angles.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\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\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eInterbedding dip angle/\u0026deg;\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e30\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e45\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003e60\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMaximum crack length/mm\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e33.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e41.53\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e71.65\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e49.32\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e28.11\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\u003eAs can be seen from Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the crack length in the interbedded rock mass generally follows a trend of first increasing and then decreasing with the dip angle, reaching its minimum at 90\u0026deg; and peaking at 45\u0026deg;.\u003c/p\u003e\u003cp\u003eThe reasons for this pattern are as follows:\u003c/p\u003e\u003cp\u003eAt 0\u0026deg;\u0026ndash;45\u0026deg;, asymmetric deformation develops gradually, but the early-stage deformation progresses relatively slowly, resulting in limited joint crack growth.\u003c/p\u003e\u003cp\u003eAt medium dip angles (around 45\u0026deg;), shear failure intensifies, and bedding-parallel slip becomes dominant, leading to a sharp increase in crack length.\u003c/p\u003e\u003cp\u003eAt 45\u0026deg;\u0026ndash;60\u0026deg;, asymmetric deformation weakens, and as the dip angle increases, the slip effect diminishes, partially suppressing crack propagation.\u003c/p\u003e\u003cp\u003eAt 60\u0026deg;\u0026ndash;90\u0026deg;, cracks are further constrained, with both crack length and distribution density decreasing, ultimately reaching their minimum at 90\u0026deg;.\u003c/p\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eAs a composite rock mass composed of multiple media, interbedded rock exhibits significant anisotropic characteristics in deformation and strength, which distinctly differ from those of homogeneous rock masses. The mechanical properties of layered rock are strongly influenced by bedding planes, the mechanical properties of the rock material, and the dip angle of the bedding planes.\u003c/p\u003e\u003cp\u003eIn this study, laboratory tests were conducted to analyze the mechanical behavior and failure characteristics of interbedded rock masses with different dip angles under high in-situ stress conditions. Additionally, discrete element analysis was employed to investigate the surrounding rock displacement, support loading, and crack propagation in tunnels with interbedded rock layers of varying thicknesses and dip angles. The following conclusions were drawn:\u003c/p\u003e\u003cp\u003e(1) The mechanical properties of interbedded rock masses are significantly influenced by the dip angle. At low dip angles, the soft layers dominate the mechanical behavior; at medium dip angles, the interfaces between soft and hard layers play a decisive role; and at high dip angles, the hard layers become predominant. With increasing confining pressure, the post-peak strain softening gradually weakens, and the ductile failure characteristics of the specimens become more pronounced.\u003c/p\u003e\u003cp\u003e(2) In uniaxial compression tests, rock masses with small dip angles undergo splitting failure, generating vertical tensile cracks that penetrate the bedding planes.At medium dip angles, shear failure occurs, producing oblique cracks that traverse the bedding planes.At high dip angles, composite failure takes place, forming both vertical tensile cracks and oblique cracks.When the thickness of the soft layer varies within a certain range, its influence on crack propagation is most pronounced.\u003c/p\u003e\u003cp\u003e(3) In the triaxial compression test, rock masses with small dip angles undergo splitting failure, with tensile cracks occurring in the hard layers;rock masses with medium dip angles exhibit shear failure, accompanied by localized tensile cracks, but the overall pattern is dominated by inclined cracks;rock masses with large dip angles experience shear failure, generating oblique cracks that penetrate the rock mass. The increase in confining pressure makes interbedded soft-hard rock masses of varying dip angles more prone to shear failure.\u003c/p\u003e\u003cp\u003e(4) Using the discrete element software 3DEC, a comparative analysis was conducted on the surrounding rock displacement, support forces, and crack propagation under different dip angles with equal layer thickness. Based on the maximum horizontal displacement difference between the left and right sides, the surrounding rock deformation was divided into four zones: the slow development zone of asymmetric deformation, the rapid development zone of asymmetric deformation, the stable zone of asymmetric deformation, and the weakening zone of asymmetric deformation. It was found that the asymmetric displacement peaks at medium dip angles (30\u0026deg;\u0026ndash;60\u0026deg;), forming small tension and large compression zones in the support structure. Additionally, crack distribution is closely related to the dip angle of interbedded layers.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eZhichun Fang, Xinyu Xu wrote the main manuscript text and prepared Figs.\u0026nbsp;1-19. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eAll data generated or analysed during this study are included in this published article\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eLi, J. H. et al. Mechanical Properties and Constitutive Model for Soft-Hard Interlayered Rock Mass. ADVANCES IN CIVIL ENGINEERING. 2024. DOI10.1155/2024/1693495. (2024).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZheng, Y. X. et al.. An Experimental Investigation on Mechanical Properties and Failure Characteristics of Layered Rock Mass. APPLIED SCIENCES-BASEL. 13, 13.DOI10.3390/app13137537. (2023).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGuo, H. et al. Mechanical analysis of toppling failure using FDEM: A case study for soft-hard interbedded anti-dip rock slope. COMPUTERS AND GEOTECHNICS. 165. DOI10.1016/j.compgeo.2023.105883. (2024).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eCui, G. Y., Qi, J. S. \u0026amp; Wang, D. Y. Research on large deformation control technology of tunnels in squeezing rock and its application. SCIENCE PROGRESS. 103, 2.DOI10.1177/0036850420923167. (2020).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYang, K. et al.. Monitoring and field tests for controlling large tunnel deformation in squeezing ground: a case study. BULLETIN OF ENGINEERING. 83, 4.DOI10.1007/s10064-024-03622-z. (2023).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWang, G. 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Rock slope stability analysis using photogrammetric data and DFN-DEM modelling.ACTA GEOTECHNICA.2015, 10, 4, 497\u0026ndash;511.DOI10.1007/s11440-015-0374-z.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLi, A. et al. Investigation Into Deformation and Failure Characteristics of the Soft-Hard Interbedded Rock Mass Under Multiaxial Compression. FRONTIERS IN EARTH SCIENCE.2022, 10. DOI10.3389/feart.903743. (2022).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"High in-situ stress, interbedded tunnel, mechanical characteristics, failure modes, discrete element analysis","lastPublishedDoi":"10.21203/rs.3.rs-7780421/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7780421/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study investigates the mechanical behavior and failure mechanisms of soft-hard interbedded tunnel under high in-situ stress, where interfacial joint planes reduce overall strength and induce anisotropy, leading to asymmetric large deformations during excavation that jeopardize construction safety and long-term operational stability. Focusing on the Jianshan Tunnel along the Zhonglan section of the Yinlan High-Speed Railway, we integrated field testing, laboratory experiments, and numerical simulations to analyze the mechanical response of interbedded rock masses at varying dip angles under high stress. Key findings include:①Field stress measurements at 342.57 m depth revealed a maximum horizontal principal stress of 12.40 MPa, with principal stress relationships SH\u0026thinsp;\u0026gt;\u0026thinsp;SV\u0026thinsp;\u0026gt;\u0026thinsp;Sh;②Laboratory tests demonstrated that the mechanical properties of interbedded rock masses are governed by the soft layer at low dip angles, by the interfacial planes at medium angles, and by the hard layer at high angles, exhibiting distinct failure modes: tensile splitting, shear failure, and composite failure, respectively;③ Numerical simulations classified surrounding rock deformation into four zones based on horizontal displacement evolution: slow-development, rapid-development, stabilization, and attenuation zones, with peak asymmetric displacement occurring at medium dip angles where minor eccentric tension and major eccentric compression regions form in supporting structures. These results provide critical insights for deformation control technologies and analogous engineering projects.\u003c/p\u003e","manuscriptTitle":"Research on Mechanical Characteristics and Failure Modes of Interbedded Rock Mass with Varying Dip Angles under High In-Situ Stress","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-29 10:47:01","doi":"10.21203/rs.3.rs-7780421/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-04-09T06:15:19+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-31T13:17:19+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"139138819896888825985231142208626525116","date":"2026-03-25T08:44:55+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"151478838858048764509249470683153213575","date":"2026-03-23T08:08:33+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-25T05:38:28+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"332635005419577847271955610481767112121","date":"2026-01-23T02:07:09+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-15T07:22:44+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-10-14T17:54:42+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-11T09:39:01+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-11T09:38:16+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-10-04T14:18:46+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"1ba9b7c5-9869-4ceb-ac62-11cf5b792aa1","owner":[],"postedDate":"October 29th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":56908987,"name":"Physical sciences/Engineering"},{"id":56908988,"name":"Physical sciences/Materials science"},{"id":56908989,"name":"Earth and environmental sciences/Solid earth sciences"}],"tags":[],"updatedAt":"2026-05-05T10:07:20+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-29 10:47:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7780421","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7780421","identity":"rs-7780421","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}