Large deformation mechanism and energy control method in carbonaceous sandy slate tunnel under high geostress

Abstract

The carbonaceous sandy slate frequently causes severe tunnel deformation and support failure during deep tunnel construction due to the coupling effects of unique physic-mechanical properties with high geostress in active tectonic zones, significantly compromising project safety and cost-effectiveness. This study systematically investigates its physic-mechanical characteristics and deformation mechanisms through laboratory testing, numerical modeling, and theoretical analysis. A methodology based on energy-absorbing principles has been proposed to control large deformations in such geological formations. The findings include: 1) the carbonaceous sandy slate exhibits significant sensitivity to moisture variations, with strength and deformation modulus markedly decreasing under saturated conditions; 2) the deformation patterns under initial support demonstrate strong dependence on both moisture states and geostress, manifesting as coupled fracturing along both vertical and bedding-parallel directions; 3) the primary mechanisms driving large deformations is buckling fractures induced by bending effects and interlayer slippage, generating compressive deformations exceeding the bearing capacity of initial supports; 4) a new yieldable cable allows controlled stress release while improving support capacity; 5) simulations show it reduces crown deformation by 34.24% and absorbs 22.13% of rock energy. This study provides theoretical and technical support for controlling large deformations in high-stress carbonaceous slate tunnels, offering practical guidance for safe construction in complex geology.

Graphical abstract

Keywords

deep tunnel / carbonaceous sandy slate / large deformation / control technology / numerical simulation

1 Introduction

The mountainous regions of western China are characterized by complex geological conditions and widely distributed layered surrounding rocks. The construction of tunnels in these regions needs to traverse complex geological environments, facing challenges such as high stress, weak and fragmented surrounding rocks, high-pressure water-rich strata, and fault fracture zones. This study focuses on in-construction tunnels in the western areas of China to investigate the deformation mechanisms and control methodologies of carbonaceous sandy slate under high geostress conditions.

As a kind of metamorphic rock rich in organic matter, carbonaceous sandy slate is prone to fragmentation and significant anisotropy under high stress, which triggers large deformation of the tunnel surrounding rock and failure of the support, seriously affecting the construction safety, progress and economy. This research systematically examines the stress-deformation characteristics of this particular rock mass through field monitoring, mechanical analysis and numerical simulation, proposing corresponding countermeasures to address these critical issues.

Regarding the investigation into the mechanisms of large deformations in layered surrounding rock, relevant studies have shown that the deformation and support damage mechanism of layered surrounding rock tunnels are significantly affected by factors such as geostress, lithology and groundwater [1–3]. Therefore, Wang et al. [4] established a limiting analysis model, the damage mechanism and failure mode of layered rocks were studied by theoretical method. Zheng et al. [5] studied the mechanical properties and damage characteristics of layered rock by model experiments. Seki et al. [6] investigated the deformation and damage patterns of the inverted arch of the tunnel under different stress conditions by modeling tests. Sun et al. [7] analyzed the large deformation of carbonaceous slate by field tests. It was concluded that different stress states, moisture condition and significant anisotropy were the main causes of large deformation.

With respect to support strategies for controlling large deformations, conventional approaches predominantly rely on rigid support systems, wherein the strength and stiffness of the support structures are utilized to constrain the deformation of the surrounding rock [8–10]. However, in many cases, excessive deformation of the surrounding rock can easily lead to failure of the support structure [11,12], resulting in the incomplete utilization of its material properties. Therefore, based on the principle of flexible support, many scholars have carried out relevant research on the yieldable structure and yield mechanism [13–15]. Among them, Lu et al. [16] developed a new type of yieldable cables applied in high geostress tunnel support to adapt to engineering applications, and tested its support effect. Sun et al. [17] proposed five negative poison’s ratio cable support schemes and conducted field tests, proving that negative Poisson’s ratio (NPR) cables with deformation-slip characteristics can effectively control the deformation of the surrounding rock. Huo et al. [18] conducted a study of NPR cables’ support characteristics through model tests and also concluded that constant-resistance slip cables can effectively control the deformation of the fragmented surrounding rock.

Existing researches have made important progress in the mechanical properties of surrounding rock, deformation mechanism and support methods, providing theoretical guidance for the construction of tunnels with high geostress weak and broken surrounding rock. However, the following deficiencies still exist.

1) The mechanical properties of different rocks vary greatly due to differences in rock composition, and the sensitivity of the mechanical properties of different rocks to the environmental conditions in the field area is significantly different, and existing studies on the physical and mechanical properties of carbonaceous sandy slate are not yet complete.

2) The effects of the time of action, disaster-causing mechanism, and environmental factors on the law of large deformation of surrounding rocks are different. The deep mechanism of large deformation of carbonaceous sandy slate tunnels under high geostress conditions needs to be further deepened.

3) Deep buried tunnel projects have special characteristics of lithology and hydrogeological environment, the existing active control technology is not applicable to this project, the flexible support mechanism and deformation control method for large deformation of carbonaceous sandy slate need to be further improved.

To address large deformation challenges in carbonaceous sandy slate tunnels, this study conducted an in-depth study on large deformation mechanism and control method based on material characterization, numerical modeling and yieldable support system. The water-induced weakening mechanism has been systematically investigated by mineral quantification X-Ray diffraction (XRD), microstructural imaging scanning electron microscopy (SEM), uniaxial tests and Brazilian splitting tests, revealing the underlying mechanism governing the variation of macro-mechanical parameters with humidity; The coupled discrete element method (DEM) and finite element method (FEM) analysis approach is used to reveal the characteristics and mechanisms of large deformation in carbonaceous sandy slate tunnels from the perspective of surrounding rock cracking.

Furthermore, based on the principle of deformation coordination and energy absorption, a new constitutive model of anchor is established, and the control effect of different support structures on large deformation of carbonaceous sandy slate is innovatively compared and analyzed by numerical experiments from the viewpoint of the energy release and accumulation of the surrounding rock. The results of this study contribute to a deeper understanding of the large deformation behavior of carbonaceous sandy slate and offer novel insights for enhancing the safety and stability of tunnel construction in such lithologies.

2 Mechanical properties of carbonaceous sandy slate and tunnel geostress

The lithology of the strata traversed by the tunnel project is predominantly composed of carbonaceous sandy slate interbedded with fractured rock masses. Based on the observed characteristics of the tunnel face, the inclination of the surrounding rock where the tunnel is situated ranges from 0° to 25° (Fig. 1). The surrounding rock exhibits a thinly layered structure with low strength and poor self-stabilizing capacity, rendering it highly susceptible to collapse. Given its overall fragility, the surrounding rock in the tunnel area predominantly belongs to Class V surrounding rock [19]. During the construction of the tunnel, pronounced large deformation phenomena were frequently observed, including tunnel face instability, twisting instability of the steel arch, and cracking of the initial support, as illustrated in Fig. 2.

Moreover, the deformation mechanism of tunnels is intrinsically governed by the physic-mechanical properties of surrounding rock and in situ stress conditions within the tunnel domain. To investigate the deformation behavior of carbonaceous sandy slate, it is imperative to elucidate the fundamental response mechanisms of tunnel deformation through comprehensive analysis of both surrounding rock characteristics and stress environment.

2.1 Anisotropic mechanical properties test

1) Specimen preparation and testing principles

To investigate the anisotropic mechanical behavior of carbonaceous sandy slate, uniaxial compression and Brazilian split tests were conducted. The rock samples were obtained from the severely deformed sections of the tunnel, where significant deformation failure such as blocks detachment, arch distortion, shotcrete cracking and other pronounced initial support failures had been observed. Subsequently, in accordance with the test methods and test standards of the international society of rock mechanics (ISRM) [20], the rock mechanical testing system was used to conduct indoor mechanical tests on the fabricated specimens. The detailed sampling procedures and criteria are shown in Figs. 3 and 4, respectively.

As shown in Fig. 4, The preparation of specimens and testing procedure follow the suggestion of ISRM [20]. The rock masses were processed into standard cylindrical specimens (diameter 50 mm × height 100 mm) and disc specimens (diameter 50 mm × thickness 25 mm) to enhance the reproducibility of the tests.

① Cylindrical specimens: the specimens were cut and polished at different structural plane angles, ensuring that the average diameter of each specimen remained within the range of (50 ± 0.15) mm, the height within (100 ± 0.3) mm, and the on-parallelism of the two end faces is less than 0.02 mm. The average diameter d_e was determined following the method illustrated in Fig. 4(c), by measuring the d₁ at distance h/5 from the top, the d₂ in the middle of the specimen and the d₃ at distance h/5 from the bottom, and the mean diameter d_e was then calculated using Eq. (1).

(1)d_{\mathrm{e}}=\frac{d_1+d_2+d_3}{3}.

② Disc specimens: To reduce the difficulty of sample preparation, disc samples were cut from cylindrical samples, as shown in Fig. 4(e). The angle of the cylindrical test specimen structure surface is selected as 90°, and after cutting and grinding, it is ensured that the surface has no obvious damage or microcracks, and is ground until there are no obvious scratches. The thickness is maintained within the specified range of (25 ± 0.1) mm, also the on-parallelism of the two end faces is less than 0.02 mm. Finally, all the specimens were wrapped in cling film to minimize the influence of transportation and environmental variations on the results of the rock mechanics tests.

The uniaxial testing method for the mechanical properties of carbonaceous sandy slate is shown in Fig. 5. The axial load was applied to the top of the specimen, while three linear variable differential transformers were employed to accurately record both axial and circumferential deformation throughout the loading process. The specimen was loaded using axial strain control at a loading rate of 0.02%/min. The loading was terminated when a significant drop in axial stress was observed—defined as a reduction exceeding 30% of the peak axial stress or when the residual strength of the specimen decreased to 70% of the peak axial stress.

For the Brazilian splitting test, the specimen was subjected to point loading, as shown in Fig. 6. The Brazilian splitting test was controlled by the displacement of the loading system with a loading rate of 0.1 mm/min. Loading was stopped once the specimen experienced brittle failure or exhibited visible cracks. The system records the rock’s peak load, from which the tensile strength of the specimen was subsequently derived using Eq. (2).

(2){\sigma }_{\mathrm{t}}=\frac{2P}{\pi dt}.

In Eq. (2), σ_t is the tensile strength (MPa); P is the ultimate force (N); d is the diameter (mm); t is the thickness (mm).

2) Rock mechanics test results

① Uniaxial results: during tunnel construction, it was observed that the water content of the rock significantly affects the anisotropic characteristics of the surrounding rock. Therefore, through the uniaxial compression test to investigate the rule of rock macro-mechanical parameters with the water content, the obtained macro-mechanical parameters under different structural plane inclinations and water content are shown in Fig. 7. Among them, The CV is the coefficient of variation of the influence of structural plane characteristics under the same water content.

As shown in Fig. 7, the compressive strength and deformation modulus of the rock exhibit substantial variation with water content under unconfined conditions. Both parameters decrease significantly as water content increases. While the effect of drying conditions on rock strength is relatively limited compared to saturated conditions, the deformation modulus shows a nearly linear decline with increasing water content.

② Brazilian splitting results: the Brazilian splitting tests were conducted to investigate the variation of rock tensile strength with water content. The splitting load and corresponding tensile strength under different inclinations and water content are shown in Fig. 8.

As shown in Fig. 8, the tensile strength of carbonaceous sandy slate varies significantly with changes in water content. In dry conditions, the effect on tensile strength is relatively limited; however, saturation leads to a substantial decrease in tensile strength. The ratio of compressive strength to tensile strength ranges from a maximum of 16.95 to a minimum of 5.30 across different water content conditions. And the primary stage of strength deterioration occurs during the transition from natural to saturated states.

2.2 Mineral composition and microstructure

Because of the high sensitivity of the engineering mechanical properties of carbonaceous sandy slate to changes in water content, and relevant studies indicate that analyzing its mineral composition and microstructure is crucial for gaining a deeper understanding of its underlying mechanisms [21,22]. Therefore, the carbonaceous sandy slate specimens with distinct structural planes were collected from tunnel sections exhibiting large deformation. The procedure for preparing is shown in Fig. 9.

During the sample preparation for mineral composition analysis, the rock specimens were crushed and ground into powder until no visible particles remained, and then passed through a 0.05 mm sieve. Two groups of samples, each weighing 15 g, and one group of samples was dried, while the other was thoroughly mixed with water and maintained in a saturated state with pressure of 105 kPa for 72 h, then the sediment was dried for group of saturated.

The microstructural analysis tests were also conducted under both natural and saturated moisture conditions. Among them, two sets of observation points, matrix and structural plane (Pre label the location), were prepared for each moisture content to observe the different structural characteristics of the rock. The sampling procedure is shown in Fig. 10.

1) Mineral composition analysis results

To accurately determine the mineral composition of the samples—particularly the content of carbonaceous material, weakly cemented substances, and water-soluble components—X-ray diffraction (XRD) tests were conducted. The scanning range for the XRD analysis was set between 5° and 90°. Two sets of samples under different moisture conditions (natural and saturated) were tested, and the mineral compositions and their volumetric ratios are shown in Fig. 11.

As shown in Fig. 11, The primary mineral components include quartz, calcite, dolomite, soda feldspar-Na, plagioclase, and white mica. The content of different mineral components determines the characteristics of the rock. Quartz minerals are the most abundant constituent of the samples, accounting for about 41% of the samples in all groups. The lowest content of both samples is calcite, which accounted for about 5 precents.

A certain amount of the clayey mineral chlorite is detected in all sample groups, and in the saturated group, Notably, the chlorite content in the saturated samples (approximately 13.6%) was lower than that in the natural condition samples (approximately 16.1%), also the soda feldspar was lower than that in the natural condition. In contrast, the contents of dolomite, calcite and white mica exhibited relatively minor variations with changes in water content (approximately 11.1%, 5.2%, and 20.25%, respectively). This indicates that exposure to water leads to partial structural mineral dissolution and reduced cementation within the rock.

Therefore, the abundant chlorite-rich clay interlayers and the sodium feldspar structure with water sensitivity within the carbonaceous sandy slate serve as the material basis for rock softening upon water exposure, while the substantial quartz content in the surrounding rock may contribute to brittle fracturing behavior during tunnel excavation.

2) Micro-structure analysis

The microscopic morphology of rocks affects the damage of rock and the deformation characteristics. In this study, the microstructure was found to have an obvious scale-like grain structure with flocculent bonding structure (Fig. 12).

As shown in Figs. 12(b) and 12(d). The carbonaceous sandy slate matrix primarily composed of massive aggregates and flocculent binders, which are mainly composed of quartz and dolomite, with uneven surface, significant development of microscopic cracks, high edge density of crystal structure, and the rock micro groups with metamorphic recrystallized massive features.

As shown in Figs. 12(a) and 12(c), the results of electron microscope scanning of the structural plane of rocks show that the degree of irregularity of the crystal surface of the structural planes is greater, and under the action of high geostress, intense geological structure and high geothermal temperature, the parts of the structural planes undergo more intense physicochemical metamorphism, the structural planes of the rocks are more unstable, and the structural integrity of the facets of the rocks is weaker, which is relatively more susceptible to the failure caused by the external conditions.

Moreover, as shown in Fig. 12, the flocculent cementing materials within the rock exhibit noticeable dissolution after saturation. SEM observations reveal a significant increase in the apparent proportion of exposed crystals under saturated conditions, indicating a marked reduction in intergranular cementation strength. This weakening of bonding between crystal clusters alters the stress transmission pathways, making the rock more vulnerable to intercrystallite damage. Notably, saturation does not result in the formation of visible seepage channels on the rock surface, which remains similar in appearance to that under natural moisture conditions. Therefore, the weakening of carbonaceous sandy slate under varying moisture levels is primarily attributed to the deterioration of bonding strength.

2.3 Geostress

The geostress measurements were carried out partially using the hydraulic fracturing method, the hydraulic fracturing mechanism is shown in Fig. 13. The water pressure for the initial cracking of the borehole is P_b, the equilibrium pressure when the crack was in a state of critical closure is P_s, the pore water pressure in the seal section is P_0.

After the initial crack was created, the water pressure was removed to close the crack, and then the crack is reopened by re-pressurizing the sealing section, noting that the pressure at the time of reopening was P_r, and then there is:

(3)S_H=3P_{\mathrm{s}}-P_{\mathrm{r}}-P_0,S_{\mathrm{h}}=P_{\mathrm{s}}={\sigma }_2.

Meanwhile, due to incomplete testing data, it is difficult to fully reflect the trend of changes in geostress with burial depth within the tunnel area. Therefore, the geostress in the tunnel area with depth was fitted, as shown in Fig. 14.

As shown in Fig. 14, The maximum and minimum horizontal principal stresses increase almost linearly with the depth of the borehole. The relationship between the three principal stresses of the borehole is characterized by S_H > S_v > S_h in the segments (S_H, S_h, and S_v are the maximum horizontal, minimum horizontal, and vertical principal stresses, respectively). This indicated that the in situ stress at the tunnel site is characterized by principal stresses acting within the transverse section. The primary factor influencing tunnel deformation is the distribution and magnitude of these in-plane principal stresses.

3 Mechanism of large deformation in carbonaceous sandy slate

The FEM, based on well-established theoretical assumptions, is effective in simulating plastic extrusion deformation in tunnel surrounding rock. However, its applicability becomes limited when studying the deformation mechanisms under complex deformation modes due to inherent theoretical constraints. In contrast, the DEM offers distinct advantages in modeling intricate deformation patterns of surrounding rock. DEM can effectively capture rock fracturing behavior, providing deeper insights into the deformation potential of surrounding rock and thereby providing a clearer understanding of complex deformation mechanisms.

3.1 Numerical modeling and parameter calibration

1) Numerical mechanics modeling

According to the on-site tunnel face exposure, the primary structural plane inclination of the strata traversed by the tunnel is approximately 15°. Taking into account the characteristics of the geostress distribution along the tunnel, the layered surrounding rock is regarded as a kind of composite material with a certain thickness of structural plane and a complete rock matrix [23]. And based on the kinematic analysis method of single-story structure proposed by Qin and Chian [24], the numerical mechanical model shown in Fig. 15 was established.

Based on on-site monitoring, the degree of large deformation exhibited by the tunnel is correlated with the burial depth of the tunnel. And the tunnel has significant high geostress and large deformation characteristics at a buried depth of about over 300 m, manifested as anisotropic distortion of the tunnel arch and partial cracking of sprayed concrete. Therefore, in order to fully consider the influence of high geostress, to investigate the influence of ground stress on rock mass deformation under different burial depths, stress under different burial depth conditions obtained by fitting were set in the boundary conditions in the model.

The numerical model of carbonaceous sandy slate was composed of finite difference grids and discrete element particles. The validity of numerical simulation results is highly dependent on the matching of particle size and grid size. If the ratio of particle size to grid size is too large, it may lead to significant distortion in the calculation results and neglect the mechanical response of boundary conditions. Conversely, if the ratio of particle size to grid size is too small, it may result in excessively high computational costs, thereby affecting computational efficiency. To ensure the accuracy of boundary condition transfer and improve computational efficiency, the sensitivity analysis of grid and particle sizes was conducted, and the minimum grid was determined to be 2.08 m, the maximum grid was 4.16 m, the minimum size of balls is 8 cm. And an anisotropic model was assigned to the grids to simulate the surrounding rock located far from the core region of the tunnel.

In the discrete element part, the blue-gray particles were used to simulate the rock matrix, the green particles were used to represent the rock structural plane, and the gray particles were used to represent the shotcrete concrete of the initial support. The structural plane used the smooth joint model; the flat joint model that can well characterize the high compressive to tensile ratio of rocks was assigned to matrix connection; the shotcrete structures were connected using the parallel bond model.

The minimum radius of particle in the core area was set to 8cm, the ratio of the maximum and minimum radius was 1.62, The initial support of the tunnel also adopts particle to simulate, with a minimum particle radius of 4 cm, a ratio of maximum to minimum radius of 1.66, and a shotcrete porosity of 0.25.

The calibration of the connections parameters was based on the structural characteristics of the carbonaceous sandy slate tunnel face exposures as well as on uniaxial compression macro-mechanical parameters at different water states. Therefore, establishing a uniaxial numerical mechanical model as shown in Fig. 16, adjusting the parameters of the model through numerical tests, and then continuously trial and error, so that the macro-mechanical parameters obtained from the numerical mechanical tests were close to the indoor tests. Comparing of the macro-mechanical parameters obtained from the comparison is shown in Fig. 17.

Furthermore, based on the rock mass deformation data from on-site monitoring and the results of laboratory tests, the maximum deformation was estimated to be 307 mm, and the micro-parameters of the rock mass were then corrected and verified. In turn, the mechanical parameters of the surrounding rock were obtained (Table 1).

3.2 Large deformation patterns in carbonaceous sandy slate

Considering the water softening characteristics of carbonaceous sandy slate and the significant variability in the behavior of carbonaceous slates similar to it in different geostress environments [25,26]. Based on the results of the calibration of the connect parameters of the surrounding rock under different water conditions and the results of the geostress test, the study on the mechanism of large deformation of the surrounding rock was carried out. Comparatively analyze the deformation convergence and rupture characteristics under different water and geostress conditions.

Meanwhile, the tunnel excavation adopted the method of full section excavation, and the initial support structure was promptly applied after the excavation. The initial support structure employs a composite system comprising a steel frame combined with shotcrete. Given the delayed strength development of shotcrete and the rapid deformation characteristics of carbonaceous sandy slate, the support strength is determined based on a reduced equivalent strength corresponding to C30 shotcrete-reinforced steel frames.

1) Influence of water contents

The softening effect of water and the weakening effect on the bond strength of matrix were considered. The parameters of each water condition obtained from the calibration were assigned to the numerical mechanical model, and the displacement of surrounding rock and initial support under different water conditions were obtained (Fig. 18).

As shown in Fig. 18, under different water conditions of the surrounding rock, the deformation of the grid and particle components were coordinated with each other. Under the structural plane feature with an angle of 15°, relatively large deformation occurred in the left shoulder of the initial support and the right invert arch, which were tangential to the structural plane. The largest was observed in the right invert arch, where it was tangential to the structural plane.

As shown in Figs. 18(a), 18(c), and 18(e), the maximum deformation of the initial support varies significantly with the water content of the surrounding rock. The maximum deformation of the initial support increases as the water content of the surrounding rock rise. The maximum displacement of the initial support was 24.32 cm under dry condition, 30.42 cm under natural condition and 40.05 cm under saturated water condition.

Meanwhile, the fracture of the surrounding rock exhibited deformation perpendicular to the structural plane and fracture in the direction of the extended structural plane, leading to a significant deflection in the surrounding rock deformation compared to the homogeneous surrounding rock under the influence of anisotropy.

After the surrounding rock was disturbed by excavation, (the black lines represent the cracks of matrix, and the red lines represent the cracks of structural plane), the degree of surrounding rock cracking gradually increased with the increase of water content. The cracks were mainly distributed near the tunnel perimeter, with the number of fractures perpendicular to the structural plane significantly exceeding those in other areas of the surrounding rock. However, it is noteworthy that in the direction of the extended structural plane, sliding and pulling action between the layers also caused a certain degree of increase in fractures along this direction.

As shown in Figs. 18(b), 18(d), and 18(f), the initial support contact force was relatively dense at the location of the left shoulder and right invert arch of the structure. Meanwhile, the contact force of the support structure was mainly based on compression, but there were also tensile contacts, and at the site of the largest contact force, the overall situation shows a mixture of tensile and compressive forces.

2) Influence of geostress

To analyze the influence of geostress on the deformation of surrounding rock, based on the established numerical mechanics model of layered surrounding rock, the damage modes of surrounding rock under different burial depths, as well as the deformation amount and deformation characteristics of the support were calculated and analyzed, so that the macroscopic deformation of the surrounding rock under the influence of surrounding rock stresses can be revealed.

In the numerical calculations, different tunnel depth conditions were used to represent the different geostress conditions. The deformation mechanism of the surrounding rock in its natural state under different burial depths (and corresponding geostress levels) was calculated and analyzed. The resulting deformation and rupture of the surrounding rock under these varying geostress conditions are shown in Fig. 19.

As shown in Fig. 19, the numerical mechanical model effectively captures the overall anisotropic deformation of the surrounding rock under extrusion at different burial depths. The largest relative deformations of the tunnel also occurred at the left shoulder and the invert arch.

Moreover, as the burial depth increased, the maximum deformation value of the tunnel surrounding rock and initial support also increased. Within the depth range from 300 to 600 m, the maximum deformation were 22.19, 31.10, 39.49 and 42.44 cm, respectively. The largest increase occurred in the 300–400 m interval, with an increase of 8.91 cm, followed by the 400–500 m interval with an increase of 8.39 cm.

The rupture pattern of the surrounding rock was generally consistent across different burial depths. Under all geostress conditions, the cracks of the surrounding rock included structural planes cracks as well as the matrix cracks. The distribution range of surrounding rock matrix cracks was mainly around the tunnel and perpendicular to the direction of the structural plane. Although some cracks extended along the structural plane direction, those perpendicular to the structural plane dominated the overall matrix crack distribution.

To further analyze the initial support force after the surrounding rock reached relative equilibrium, the calculated deformation and contact force under different burial depth were analyzed, the results are shown in Fig. 20.

As shown in Fig. 20, the deformation and force chains of the initial support exhibited significant anisotropic characteristics. In initial support, compressive forces play a dominant role, although some localized areas experience tensile contact. The contact forces are most concentrated at the left shoulder and the invert arch, where tensile forces are also relatively high.

3.3 Large deformation mechanism of carbonaceous sandy slate

The tunnel failure in carbonaceous sandy slate is characterized by rapid and large deformation, along with complex instability modes. According to the indoor tests have shown that carbonaceous sandy slate exhibits significant water-induced softening and pronounced brittle fracture mechanical properties. As demonstrated by the analytical results in Subsection 2.2, water infiltration and erosion weaken and dissolve the cementing materials in rocks. Under the combined effects of geostress and engineering unloading, the interlayer separation, also bending and slide deformation of surrounding rocks intensify with increasing water content. Based on the Figs. 18 and 19, the deformation mechanisms of carbonaceous sandy slate can be deconstructed through numerical calculation and theoretical analysis (Fig. 21).

As shown in Fig. 21, the deformation of the surrounding rock can be categorized into two components: deformation perpendicular to the structural plane and deformation along the extended direction of the structural plane. The perpendicular deformation is mainly caused by interlayer bending under the extrusion of geostress, while the deformation along the structural plane results from the failure of the structural plane and interlayer sliding.

Generally speaking, the large deformation disaster of surrounding rock is mainly caused by the deformation both perpendicular and parallel to the structural plane of the surrounding rock after the tunnel excavation. Under the disturbance, the rock is affected by water, causing weakening of the matrix cementation and exacerbating the potential for failure in the vertical structural plane direction. And under high geostress, the rock experiences bending, rupture, and interlayer slippage, resulting in extrusion and deformation that exceed the bearing capacity of the support system, eventually leading to support failure and posing a serious threat to tunnel safety and stability.

4 Methods of controlling large deformations in carbonaceous sandy slates

Based on the deformation characteristics of carbonaceous sandy slate, its deformation has strong continuity under the support effect, and its large deformation is often accompanied by significant energy release and displacement. Conventional support measures are difficult to accommodate such deformation, leading to a loss of overall bearing capacity before the support structures can fully utilize the mechanical properties of their materials. Therefore, the large deformation control method of carbonaceous sandy slate should mainly research from the perspective of coordinated deformation, energy absorption and pressure relief.

Therefore, the finite difference numerical analysis method was used to calculate the deformation and relative deformation of the surrounding rock under various cable support conditions, and to analyze the control effect of different cable support structure forms on the large deformation of the surrounding rock based on the perspective of the surrounding rock displacement and the surrounding rock strain energy.

4.1 Energy evolution in surrounding rock

Assuming that the layered surrounding rock is isotropic and homogeneous at a given point, the surrounding rock reaches a new equilibrium state by releasing energy after being disturbed by tunnel excavation. The energy distribution during the load-bearing process within the surrounding rock unit is shown as Fig. 22.

As shown in Fig. 22, the energy input into the surrounding rock by external loads is partially converted into internal energy and partially into kinetic energy. Additionally, the deformation of the surrounding rock leads to temperature changes and heat exchange with the external environment. Therefore, the energy caused by the engineering activities in the surrounding rock can be described by the first law of thermodynamics:

(5)U=U^{\mathrm{d}}+U^{\mathrm{e}}+Q.

In Eq. (5), U is the energy generated by the engineering effect; U^d is the kinetic energy; U^e is the internal energy; and Q is the thermal energy exchange between the surrounding rock and the outside environment.

In engineering construction, the thermal energy exchange between the surrounding rock and the outside environment is relatively small compared to the change of kinetic and internal energy. Based on the relationship between elastic energy and stress, the following expression can be derived:

(6)U=\int {\sigma }_1\mathrm{d}{\epsilon }_1+\int {\sigma }_2\mathrm{d}{\epsilon }_2+\int {\sigma }_3\mathrm{d}{\epsilon }_3,

(7)U^e=\frac{1}{2}{\sigma }_1\mathrm{d}{\epsilon }_1^e+\frac{1}{2}{\sigma }_2\mathrm{d}{\epsilon }_2^e+\frac{1}{2}{\sigma }_3\mathrm{d}{\epsilon }_3^e.

In Eqs. (6) and (7): σ_i is the principal stress of the surrounding rock unit; ε_i is the principal strain in the direction of the principal stress of i; ε_e is the elastic strain of the surrounding rock. And the elastic strain can be expressed as the expression form of the principal stress tensor of the unit, specifically as shown in Eq. (8), and thus the elastic strain energy can be expressed as the form of the principal stress tensor shown in Eq. (9):

(8){\mathit{\epsilon }}_i^{\mathrm{e}}=\frac{1}{E_i}\left[{\mathit{\sigma }}_i-{\nu }_i\left({\mathit{\sigma }}_j+{\mathit{\sigma }}_k\right)\right],

(9)U^{\mathrm{e}}=\frac{1}{2E_0}\left[{\sigma }_1^2+{\sigma }_1^2+{\sigma }_1^2-2\nu \left({\sigma }_1{\sigma }_2+{\sigma }_2{\sigma }_3+{\sigma }_1{\sigma }_3\right)\right].

In Eq. (9): σ_i is the principal stress tensor of the surrounding rock unit; v, E₀ are Poisson’s ratio and short-term modulus of elasticity, respectively.

As the tunnel surrounding rock is disturbed by excavation activities, the stress state undergoes redistribution. During this process, the principal stress tensor of the surrounding rock units changes significantly, resulting in a corresponding variation in their elastic strain energy. The energy input from excavation is mainly transformed into internal energy (elastic strain energy) and kinetic energy (displacement potential energy).

4.2 Support mechanism of yieldable cable

To solve the problem of excessive deformation of the surrounding rock that causes premature failure of conventional cable supports and the problem of the cables from fully utilizing their mechanical properties. Based on the principle of active support and energy-absorbing, a yieldable cable support system, which was capable of absorbing part of the energy released during the equilibrium process of the surrounding rock after excavation disturbances was proposed.

Through the deformation of the yieldable device to achieve the large deformation of the cable under constant resistance conditions, enhance the ability of the cable to adapt to the deformation of the surrounding rock, to achieve the purpose of improving the support capacity of the cable, and then significantly reduce the amount of convergence. The design and performance test results [27] and the working principle are shown in Figs. 23 and 24, respectively.

As shown in Figs. 23 and 24, the mechanical mechanism of yieldable cable can be divided into 4 stages: 1) OA stage: the initial hardening stage, because of threshold damping, the cable pullout force and displacement showed linear relationship; 2) AB stage: the yield stage, the axial force increases at a low rate until it reached the designed maximum displacement; 3) BC stage: the second hardening stage, under the effect of yield stopper, internal force of cable increased rapidly; 4) CD stage: the failure instability stage, the force reached the peak and the rod tensile yielding to failure.

In the support, cable provide support mainly in the axial direction of the cable, and the axial force of the cable close to the tunnel surface is the supporting force of the cable.

Regarding the mechanical response of layered surrounding rock, the assumptions adopted in this study are as follows: 1) the structural planes in the surrounding rock are modeled as thin layers with negligible thickness, where the marked contrast in strength and stiffness between these layered discontinuities and the intact rock matrix induces significant anisotropy in the overall rock mass behavior; 2) divide the layered surrounding rock into multiple bands with a width of dθ, starting from the center point of the tunnel. In a certain band, the spacing between structural planes is fixed; 3) the weakening effect of structural planes on the matrix in each band is the same.

Therefore, according to the principles of elastic-plastic mechanics, the boundary between the plastic zone and the elastic zone in the direction of the strip can be calculated. Due to the fixed structural characteristics of the structural planes, changes in the strip angle will affect the number of structural planes within the same length range. If the angle direction of the vertical structural plane is taken as the 0° direction, then within the range of 0°–90°, as the angle increases, the weakening points of the structural plane within the same strip length range become fewer, and the strength and stiffness of the surrounding rock strip are closer to homogeneous surrounding rock. The interlayer spacing of the surrounding rock can be expressed as Eq. (10).

(10)h^{\prime }=\frac{h}{\cos \alpha }.

Furthermore, the larger the spacing between the structural planes corresponding to the angle, the greater the strength and stiffness of the surrounding rock. Therefore, the layered surrounding rock can be equivalent to uniform surrounding rock, and its specific strength parameters are converted as shown in Eqs. (11)–(13). The stress resolution of the surrounding rock is shown in Fig. 25.

(11)c^{\prime }=c\left(1-\frac{{\lambda }_{\mathrm{c}}\cos \alpha }{h}\right),

(12){\phi }^{\prime }=\phi \left(1-\frac{{\lambda }_{\phi }\cos \alpha }{h}\right),

(13)E^{\prime }=E\left(1-\frac{{\lambda }_{\mathrm{E}}\cos \alpha }{h}\right),

where h is the structural plane distance; c is the matrix cohesion; c^{\prime } is the equivalent cohesion of layered surrounding rock; φ is the matrix friction angle; {\phi }^{\prime } is the equivalent friction angle of layered surrounding rock; E is the matrix elasticity modulus; H^{\prime } is the equivalent elasticity modulus of layered surrounding rock; α is the angle between the strip where the microelement is located and the perpendicular structure plane direction; λ_c, λ_φ and λ_E is the cohesion, friction angle and elastic modulus- reduction factor, respectively.

Therefore, according to the deformation compatibility principle and stress resolution, the explicit relationship between the displacement of surrounding rock and support force is obtained:

(14)\begin{array}{rl}{u}_{\mathrm{R}}=& \frac{R\left(p_0\sin {\phi }^{\prime }+c^{\prime }\cdot \cos {\phi }^{\prime }\right)}{2G}\\ & \cdot {\left[\frac{\left(p_0+c^{\prime }\cdot \cot {\phi }^{\prime }\right)\left(1-\sin {\phi }^{\prime }\right)}{p_i+c^{\prime }\cdot \cot {\phi }^{\prime }}\right]}^{\frac{1-\sin {\phi }^{\prime }}{\sin {\phi }^{\prime }}},\end{array}

where p₀ is the far site stress of the surrounding rock; R is the radius of the tunnel; G is the shear modulus of the layered surrounding rock; p_i is the tunnel support force, which is related to stress release, and it can be regarded as the sum of virtual support force [28] (stress release related) and support structure resistance. In turn, the support force−deformation generalization curve can be obtained as follows Fig. 26.

4.3 Validation of control method based on energy-absorbing

1) 3D numerical mechanical model and the yield constitutive

To consider the influence of the stress release of the surrounding rock during the longitudinal excavation process on the large deformation of the carbonaceous sandy slate, based on the maximum value of the deformation convergence of the tunnel in the natural state, a finite difference numerical simulation method was used and a numerical mechanical model was established (Fig. 27), and the parameters of the model were calibrated, the convergent deformation of the surrounding rock was monitored in the subsequent simulation process.

The anisotropic elastic-plastic model (Ubiquitous joint model) was assigned to the rock, its parameters are shown in Table 2. And the isotropic elastic model was assigned to the support structure.

In the tunnel design, the maximum effective range of the support extends 15–30 m ahead of the tunnel face. It is assumed that beyond this range, the excavation has minimal impact on the surrounding rock. To more comprehensively understand the mechanical response of the surrounding rock throughout the excavation process, the monitoring section of the model was selected to be 29.5 m ahead of the tunnel face (10th step of the tunnel).

Meanwhile, in order to compare the control effects of different types of cable on carbonaceous sandy slate and to calculate the deformation of the surrounding rock under different types of cable conditions, based on the structural characteristics and mechanical properties of the yieldable cable, the constitutive model of the yieldable cable was developed and successfully implemented in the finite difference calculation software. The constitutive relationship of the compression anchor is given in Eq. (15) and the mechanical parameters of the cable materials are listed in Table 3.

(15)

In the formula, ε is the axial strain, ε₁ is the yield start strain, ε_R is the yield end strain, ε_f is the failure strain, E₁ is the deformation modulus at the initial hardening stage, E_R is the deformation modulus at the yield stage, E₂ is the deformation modulus at the second hardening stage, F_R is the threshold of yield.

2) Comparison of numerical calculation results

Based on the established numerical mechanical model of large deformation in the tunnel, a comparative analysis was conducted to investigate the influence of different support conditions on the large deformation behavior of the surrounding rock. And the relative deformation is widely used in practice [29,30]. Therefore, the relative deformation was used in this study and quantified using the Von Mises equivalent strain increment, as expressed in Eq. (16).

(16)\begin{array}{rl}& {\epsilon }_{\mathrm{V}\mathrm{o}\mathrm{n}-\mathrm{M}\mathrm{i}\mathrm{s}\mathrm{e}\mathrm{s}}\\ =& \sqrt{{\epsilon }_{xx}^2+{\epsilon }_{yy}^2+{\epsilon }_{zz}^2-{\epsilon }_{xx}{\epsilon }_{yy}-{\epsilon }_{xx}{\epsilon }_{yy}-{\epsilon }_{yy}{\epsilon }_{zz}+2\left({\epsilon }_{xy}^2+{\epsilon }_{yz}^2+{\epsilon }_{zx}^2\right)}.\end{array}

This method provides a more comprehensive and objective representation and comparison of the magnitude of strain increments in different regions and is particularly suitable for assessing the yield or plastic deformation behavior of geotechnical materials. The obtained deformation and the longitudinal displacement profile (LDP) curves are shown in Figs. 28 and 29, respectively.

From Figs. 28 and 29, at the no cable support condition, the maximum relative deformation was 6.75%, and the maximum deformation of the surrounding rock was located in the left arch (vertical structural plane) and the inverted arch, with the maximum deformation of 34.63 and 42.91 cm, respectively. While the deformation of the two hance and the wall corners were relatively small.

After applying ordinary cable, pre-stressed cable and yieldable cable, the deformation and the relative deformation of surrounding rock in each part of the tunnel were reduced to varying degrees. At the location of maximum deformation at the tunnel crown, the deformations corresponding to the ordinary cable, pre-stressed cable, and yieldable cable were 34.19, 31.65, and 22.77 cm, respectively. The percentage of reductions relative to the no cable condition were 1.26%, 8.62%, and 34.24%, respectively. A comparative analysis of the working conditions and force states of the cables under different support types is presented in Fig. 30 (the cable force label is based on all cable forces globally).

As shown in Fig. 30, Under different support schemes, the operating conditions and mechanical responses of cables exhibit significant differences. The ordinary cables installed in steps 1 to 29 have basically lost their suspension load-bearing capacity, while only the cables at the crown of the pre-stressed cables in steps 1 to 28 have lost their suspension load-bearing capacity. For both ordinary and pre-stressed cables, they lack effective stress regulation mechanisms, making it difficult for them to dissipate energy through plastic deformation during large deformations. When axial strain exceeds the material’s limit, the cable may experience localized necking, broken wires, or even complete rupture, ultimately leading to structural failure.

Under the yieldable cable condition, the surrounding rock convergence was intensified, and the axial force of the cable reached the yield threshold, the yield action started. The cables deformed coordinately with the surrounding rock, so that the cable support ability and the mechanical properties of the rod material continue to play a role in the support and then realize the effect of yieldable cables to reduce the large deformation of the surrounding rock significantly. Meanwhile, the surrounding rock elastic strain energy U^e in the monitoring section (y = 29.5 m) are shown in Fig. 31.

From Fig. 31, it can be observed that the maximum unit volumetric strain energy value of the surrounding rock varied significantly under different support conditions, although the overall distribution pattern of strain energy along the surrounding rock section remained generally similar.

The areas of relatively high strain energy accumulation were primarily located in the crown and the bottom areas at a certain distance from the tunnel center. The yieldable cable support resulted in the lowest strain energy accumulation in the surrounding rock, while the pre-stressed cable support showed intermediate energy levels. In contrast, the ordinary cable support only marginally reduced strain energy compared to the unsupported condition.

Meanwhile, the evolution law of the maximum unit strain energy cumulative-release of the section was analyzed under different cable support conditions, the results are shown in Figs. 32 and 33.

As shown in Fig. 32, Since ordinary cables have poor deformation adaptability and low capacity to absorb deformation through their own plastic deformation, the strain energy evolution curves of the surrounding rock under the no-cable and ordinary cable conditions were almost identical; The deformation capacity of pre-stressed cable is slightly enhanced. Meanwhile, some cables that have not failed will play a certain role in the longitudinal direction of the tunnel, so under the condition of pre-stressed cable, the strain energy evolution curve of the surrounding rock was relatively reduced. The yieldable cable has the strongest deformation capacity, and the cable is basically in a normal working state, the strain energy evolution of the cable was significantly reduced with the yieldable cable condition.

The variation of strain energy in the monitoring section exhibited both energy accumulation and release throughout the tunnel excavation process. The strain energy exhibited a gradual accumulation before the monitoring section excavation. And at the 6th step of the excavation (9 m ahead of the monitoring section), the monitoring section experienced the maximum rate of strain energy accumulation due to the disturbance caused by the preceding excavation activities.

However, when the excavation was 2 steps away from the monitoring section (the excavation section was 6m away from the monitoring section), the energy in the monitoring section showed a macroscopic trend of energy release, with the released energy exceeding the accumulated energy. The maximum energy release occurred when the excavation was one step (3 m ahead of the monitoring section). After the excavation of the monitoring section, the energy release gradually approached zero. With continued excavation, the energy release became smaller than the accumulated energy, and the strain energy of the surrounding rock gradually increased and then tend to stabilize. The comparison of maximum strain energy and deformation under each condition are shown in Figs. 34 and 35, respectively.

As shown in Figs. 34 and 35, during the tunnel excavation and support process, ordinary cables and pre-stressed cables were unable to endure the internal force of cables caused by the surrounding rock deformation, resulting in support failure. While yieldable cables slipped during the support process, continuously suspending the surrounding rock and converting the energy released during the rock equilibrium process into the deformation kinetic energy of the rock and the energy absorbed by cable deformation. Therefore, once the surrounding rock stabilized under the yieldable cable support, its energy was significantly lower than that of surrounding rock supported by ordinary or pre-stressed cables.

Under the conditions of ordinary cable, pre-stressed cable, and yieldable cable, the cable support system was able to absorb 0.48%, 3.54%, and 11.76% of the maximum strain energy, respectively. In addition, the excavation caused the adjustment of surrounding rock, the rock became more active, and the energy became more and more, both the deformation of the surrounding rock and that of the cables contributed to energy absorption. By analyzing the difference between the stabilized and initial energy values (i.e., the jump energy), it was found that ordinary cables, pre-stressed cables, and yieldable cables could reduce the jump energy by 0.90%, 6.66%, and 22.13%, respectively. Therefore, yieldable cables can significantly improve the force situation and reduce the subsequent deformation potential of the surrounding rock of carbonaceous sandy slate.

5 Conclusions

Taking the carbonaceous sandy slate tunnels under construction in the mountainous areas of western China as a case study, this research systematically reveals the physical and mechanical properties and deformation damage mechanism of carbonaceous sandy slate through indoor tests, discrete element numerical simulations and theoretical analyses. A control method based on energy-absorbing to adapted the large deformation of carbonaceous sandy slate was proposed and experimentally investigated by numerical mechanics, the conclusions of the study are as follows.

1) The physical and mechanical properties of carbonaceous sandy slate are significantly affected by water content. The compressive strength, tensile strength, and deformation modulus decrease more sharply under saturated conditions than from dry to natural states. This weakening effect is primarily attributed to the dissolution and softening of matrix intercrystallite cementation structures upon contact with water.

2) The deformation of the surrounding rock is significantly affected by the water content and geostress. Higher water content and deeper burial depth lead to increased deformation. Under dry, natural and saturated conditions, the maximum deformation of surrounding rock were 24.32, 30.42, and 40.05 cm, respectively; the maximum deformation of surrounding rock under 300–600 m burial depth geostress condition were 22.19, 31.10, 39.49, and 42.44 cm, respectively.

3) Surrounding rocks in different water conditions and geostress conditions are presented in the vertical and extended structural plane direction coupled with the characteristics of broken deformation. The main cause of large deformation disasters in carbonaceous sandy slate tunnels is that the supporting structure cannot withstand the squeezing effects caused by bending fractures and interlayer slippage.

4) Based on the principle of energy dissipation and deformation coordination, the proposed yieldable cables can significantly improve the stress environment and deformation adaptability of the surrounding rock. It enables a synergistic enhancement of both controllable deformation release and support bearing capacity. Numerical simulations show that the yieldable support can reduce the maximum deformation of the tunnel by 34.24% and absorbs 22.13% of the jump energy of the surrounding rock units.

This study provides a theoretical foundation and key technical support for the prevention and control of large deformations in high-geostress carbonaceous sandy slate tunnels. It holds significant importance for ensuring the safety of tunnel construction under complex geological conditions.

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