With the continued implementation of the western development strategy, the economy of the less developed areas in the west has been developed rapidly and various transportation networks have been improved (Li et al. 2022). In recent years, a large number of railroads and high-speed lines have been built in the western region one after another. However, because the western region is located at the junction of different plates, the mutual extrusion process of the plates during the long geological era has made the western region present complex mountainous and plateau topographic features. During the tunnel construction process, the number and scale of tunnels leading to long, difficult and complex conditions in the mountain ranges continue to increase, and with them various geological hazards such as high ground stress, rock bursts, sudden water and mud surges, and large deformations in soft rocks also occur frequently, posing a huge challenge to the safety of tunnel construction (Yu et al. 2022). Large deformation of the surrounding rock is one of the most serious engineering hazard phenomena during the construction of mountain tunnels in the western region (Xia et al. 2021).

Many scholars at home and abroad have conducted many studies on the control of tunnel envelopes. Hoek and Guevara (2009) studied the problem of large deformation of extruded surrounding rocks in tunnels with high ground stress, and proposed a pressure-allowing support technology with a retractable steel arch with slip grooves as the core.Lai et al. (2015) verified the conclusion that the three-layer support structure is effective in supporting tunnels through field experiments. Song and Sun (1991) studied the deformation mechanism of the surrounding rock in underground space and concluded that the jet anchor support helps to stabilize the surrounding rock. Zheng et al. (1993) proposed the soft rock control technology of "anchor spraying—high strength reinforced concrete arc plate" based on the joint support theory of "flexible + high strength rigid". Li (2011) successfully controlled the large deformation disaster of surrounding rocks in high ground stress soft rock tunnels by improving the stiffness of the support system and increasing the reserved deformation volume for the phenomenon of large deformation of thin laminated carbonaceous slate. Zhou et al. (2013) in order to study the control countermeasures for large deformation of the surrounding rock in soft rock tunnels in strong seismic areas, the optimal support technology based on overrunning small conduit, anchor network spray frame, pre-deformed volume and reinforced concrete lining was derived. By establishing a similar physical model, Li et al. (2023a, b) has deeply studied the problem of roadway stability in deep underground engineering. Seo et al. (2014) used an overrunning soil nail support technique to improve the stability of the working face to reduce tunnel deformation in response to the problem of easy collapse in Qianbei tunnel excavation. Merlini et al. (2018) adopted a support scheme of sprayed anchor support, fiber reinforced shotcrete and steel arch, which effectively controlled the deformation of the surrounding rock. Ming et al. (2023) studied the supporting effect of energy-absorbing anchor cables on asymmetric tunnels through numerical simulation.

The above-mentioned scholars have made outstanding contributions to the study of roadway support, but have limited effect on the control of large deformation of surrounding rock in fractured tunnels. In this paper, Minxian tunnel containing strongly weathered carbonaceous slate is used as the engineering background, and indoor tests (rock microstructure and mineral analysis experiments, NPR anchor cable mechanics experiments), FLAC3D numerical simulation experiments and field monitoring (ground stress monitoring experiments, stress–strain experiments after NPR anchor cable support) are used for the study. It provides a scientific basis for the study of other soft rock large deformation tunnels.

2.1 Ground stress analysis

Three cross-sections, mileage K235 + 090, K235 + 170 and K235 + 300, were selected for ground stress testing in the right tunnel of Minxian Tunnel, which corresponded to a tunnel burial depth of about 165 m, 190 m and 200 m, respectively. The test results are shown in Table 1. From the ground stress test results, the ground stress distribution pattern of Minxian tunnel can be obtained.

1. (1)

   All three measurement points have two main stresses close to the horizontal direction, and the average angle with the horizontal plane is 8.362°, the minimum is 3.128°, and the maximum is 13.584°. The other principal stress direction is close to the vertical direction, with an average angle of 75.74° with the horizontal plane, reaching a maximum of 83.462°.

2. (2)

   The stress state in the Min County tunnel is σ_H > σ_v > σ_h, that is, the maximum horizontal principal stress > vertical principal stress > minimum horizontal principal stress. The ratio of the maximum horizontal principal stress to the vertical stress is usually defined as the lateral stress coefficient, which is 1.312 ~ 1.350 for the Min County tunnel. Therefore, it can be seen that the effect of tectonic stress field along the Minxian tunnel is more obvious, which is also in line with the formation characteristics of Minxian-Dangchang complex oblique and cooperative-Minxian fracture tectonic zone.

3. (3)

   The direction of the maximum horizontal principal stress is north-northeast—west-southwest, in the direction of about EN43° to 52° range. The tunnel boring direction is near NS direction. The maximum horizontal principal stress has the greatest impact on the stability of the tunnel when it is perpendicular to the axial direction of the tunnel. When the maximum horizontal principal stress is parallel to the axial direction of the tunnel, its effect on the stability of the tunnel is minimal. For the Min County tunnel, the maximum horizontal principal stress has a certain influence on the stability of the tunnel.

4. (4)

   The measured vertical stresses at the three measurement points are 4.133 MPa, 4.267 MPa, and 4.615 MPa, respectively. The density of carbonaceous slate is about 2360 kg/m³, and the weight of the corresponding overlying rock is 3.894 MPa, 4.484 MPa, and 4.72 MPa, respectively, according to the burial depth of three points. The errors were 6.14%, 4.84%, and 2.23%, respectively, which were very small. Therefore, the weight of the overlying rock layer can be used as the vertical stress calculation in the remaining locations.

2.2 Microstructure and mineral composition of tunnel surrounding rocks

In order to study the mineral composition of carbonaceous slate, carbonaceous slate blocks were randomly selected at different mile locations (YK235 + 475, YK235 + 480, YK235 + 485, YK235 + 490, YK235 + 495) in the right line of Minxian tunnel, and the selected samples are shown in Fig. 1.

Powder samples of surrounding rocks (Tao et al. 2020)

The OLYMPUS-BX53 rock and mineral identification instrument was used to identify 12 rock block thin sections. The results show that the selected flakes are mainly strongly weathered carbonaceous slate and moderately weathered carbonaceous slate.

The strongly weathered carbonaceous slates are mainly composed of siliceous, clayey, carbonaceous, and terrigenous clasts (Fig. 2a).Most of the clayey and carbonaceous materials are mixed together and distributed, and some of them are relatively aggregated like streak-like distribution respectively. The clayey texture consists of clay minerals < 0.005 mm, with some transformation to microscale sericite, with obvious long axis orientation (Fig. 2b). The charcoal is in the form of dusty spots. The terrestrial source debris is composed of quartz and white mica, mainly white mica, unevenly distributed, and the particle size is generally 0.02–0.15 mm. The quartz is sub-angular in shape and the white mica is scaly. Sericite filled fissures and veinlets are seen within the rock (Fig. 2c) and have undergone tectonism along with the rock, which was later subjected to folding (Fig. 2d).

Microstructural characteristics of strongly weathered carbonaceous slate

The fresh surface of the medium-weathered carbonaceous slate is black, with slab-like structure and variably laminated structure (Fig. 3a), and the rock has a cryptocrystalline structure (Fig. 3b). It is mainly composed of siliceous, clayey, ferrocarbonous, and terrestrial-derived debris. Siliceous mixed with clayey, siliceous composed of cryptocrystalline chalcedony, partially recrystallized into particulate quartz. The clayey texture consists of < 0.005 mm clay minerals, which partly change to microscale sericite, mostly showing long axis orientation (Fig. 3c). The iron carbonaceous material is in the form of dusty dots, unevenly mixed within the rock. The terrigenous debris consists of quartz and sericite, which are scattered and generally 0.02–0.08 mm in size, with sub-angular quartz and scaly sericite (mostly long-axis oriented), and carbonate-filled fractures are visible within the rock (Fig. 3d).

Microstructural characteristics of moderately weathered carbonaceous slate

In order to further understand the mineral composition of the carbonaceous slate and its relative content accurately, the whole-rock mineral content analysis was performed on the strongly weathered carbonaceous slate and the moderately weathered carbonaceous slate selected from the above-mentioned thin sections, respectively. The analysis was carried out using an Empyrean sharp shadow and X-ray diffractometer, and the rocks were analyzed by X-ray diffraction of common minerals according to the "K-value method".

All common mineral crystals in rocks have their specific X-ray diffraction patterns, and the intensity of the characteristic peak in the pattern is positively correlated with the amount of that mineral in the rock sample. Mineral samples with different particle sizes in mineral powders were separated and extracted by centrifugation, and then, the different minerals were subjected to X-ray diffraction. Analysis of the diffraction results against a specific diffraction pattern and its peak intensity characteristic values gives an accurate picture of the mineral composition of the sample and its relative content.

Five samples were selected for whole-rock mineral X-ray diffraction analysis, and the results are shown in Table 2. After whole-rock mineral composition analysis of the rock samples, it was found that the mineral composition of strongly weathered carbonaceous slate and moderately weathered carbonaceous slate were basically the same, but the relative contents of different minerals were different. The carbonaceous slate is mainly composed of quartz and clay minerals, and the average content of both reaches over 85%, with quartz content ranging from 35.2% to 68.6% and clay mineral content ranging from 18.6% to 55.1%.

Clay minerals are a class of mineral components formed by the chemical weathering of aluminosilicate minerals such as feldspar and mica, which have the property of absorbing water and softening and swelling. Depending on the ratio of internal basic units, clay minerals are divided into three main groups, namely kaolinite, montmorillonite and illite. Different types of clay minerals have different softening properties, and the presence of clay minerals largely determines the nature of the soft rock.

2.3 Acoustic testing of tunnel boreholes

As shown in Fig. 4, acoustic monitoring was performed on six cross sections in two areas with a maximum depth of 30 m boreholes. Based on the acoustic test curves in the borehole, the envelope structure of the section can be divided into approximately 2 zones:

1. (1)

   Within the range of 0 ~ 8 m from the surface of the surrounding rock, the wave speed of the surrounding rock fluctuates within the range of 1000 ~ 2000 m/s, only at the depth of 5 m the wave speed reaches 2000 m/s, and the wave speed of the surrounding rock at the rest of the location is around 1300 m/s. Therefore, the fracture degree of the surrounding rock in this range is high, and the structural weak surface in the rock body is developed and open, and the range is judged to be the excavation disturbance zone of the surrounding rock, and the division between the residual strength destruction zone and the plastic zone is not obvious.

2. (2)

   The deep rock body in the range > 8 m from the surface of the surrounding rock, the wave speed of the surrounding rock fluctuates between 1000 ~ 4000 m/s, and most of the locations fluctuate around 2000 m/s. Therefore, it can be considered that the surrounding rock within this area is little affected by the tunnel excavation, the surrounding rock structure is relatively intact and the surrounding rock is in an elastic state.

Acoustic wave test results of loose section

According to the acoustic measurement results and analysis of the above boreholes, the acoustic velocity curve of the surrounding rock in the large deformation section of the Minxian tunnel shows three obvious regions, namely the damage zone, plastic zone and elastic zone, due to the different degrees of fragmentation of the surrounding rock, as shown in Fig. 5.

1. (1)

   Destruction area Within 0 ~ 4 m from the surface of the surrounding rock, the weak surface of the surrounding rock such as slab fissures is completely extended and penetrated, the rock body is broken to a high degree and basically loses bearing capacity, and the rock body is in the post-peak residual deformation stage. Therefore, it is also called the residual strength zone or plastic flow zone.

2. (2)

   Plasticity zone Within 4 ~ 10 m from the surface of the surrounding rock, the expansion and extension of the weak surface of the surrounding rock, such as plate fractures, increases the degree of rock fragmentation, the rock yields under the action of high concentrated stress and enters the softening stage after the peak, the rock has a certain bearing capacity, called the plastic zone (plastic softening zone).

3. (3)

   Resilient zone The deep area > 10 m from the surface of the surrounding rock is less affected by excavation disturbance, the concentrated stress caused by stress adjustment and transfer is smaller, the surrounding rock in the area is in the pre-peak plastic hardening section or elastic stage, and the surrounding rock is still in a stable state.

Three zones of surrounding rocks of the tunnel

The above analysis shows that the extent of the damage zone and the plastic zone of the surrounding rock is determined by the magnitude of the ground stress and the mechanical properties of the rock mass. Although the strength of the rock mass is high, the nodular structure leads to a substantial reduction in the integrity of the rock mass and a substantial reduction in the strength of the rock mass. Therefore, although the burial depth of Minxian tunnel is not large, the surrounding rock still produces significant large deformation under lower ground stress, and the development of structural surfaces leading to laminated slate fragmentation and jointing is the most important reason for the large deformation of soft rock in Minxian tunnel.

Engineering excavation is the root cause of large deformation disaster of tunnel surrounding rock. After tunnel excavation, the radial stress σ₃ of the tunnel surrounding rock is 0, and the tangential stress σ₁ will be concentrated. Under the condition of hydrostatic pressure, the tangential stress σ₁ will increase to twice, exceeding the strength envelope of the surrounding rock. At this time, the failure of the surrounding rock leads to the occurrence of large deformation disasters, and the stress state of the rock mass changes from the three-dimensional stress state to the two-dimensional or one-dimensional stress state. Excavation compensation method is conducive to applying high prestress compensation in time after tunnel excavation, restoring the three-dimensional stress state of surrounding rock, obtaining higher rock bearing capacity, and reducing the damage of surrounding rock.

The compensatory mechanical behavior of NPR anchor cables is the key to tunnel support, so this section investigates the super-mechanical properties of NPR anchor cables. In order to prevent rock collapse in the mining area, the most intuitive and effective way of engineering is currently anchor cable support for the surrounding rock (Xia et al. 2021). NPR anchor cable utilizes the negative Poisson's ratio effect, which is a new type of anchor cable with stronger support effect than traditional anchor cable. The NPR anchor cable mainly consists of steel strand, constant resistance body, constant resistance casing, tray and anchorage, as shown in Fig. 6.

Structure composition of NPR anchor cable (Li et al. 2023a, b)

3.1 Constitutive relation of NPR anchor cable

Radial friction is generated when the constant resistance body within the NPR anchor cable moves within the constant resistance casing, and the maximum friction generated is referred to as the critical resistance P₀, and is given by (He et al. 2016):

where f is the static friction coefficient of the constant resistance body slipping in the casing, I_s is the material parameter of the constant resistance casing, I_c is the geometric parameter of the constant resistance body, and its formula is shown as follows:

where, \(\alpha\) is the inclination angle of the bevel of the constant resistance body, \(h\) is the length of the constant resistance body, a and b are the diameters of the small and large ends of the constant resistance body respectively, E and \(\mu\) is the elastic modulus and Poisson's ratio of the casing.

From Eq. (3), it can be seen that the critical resistance P₀ of NPR anchor cable is only related to f, I_s and I_c, and is independent of the external load, so P₀ is also called the constant resistance of NPR anchor cable.

The mechanical relationship of NPR anchor cable follows the criterion of Hooke's law. When the anchor cable is displaced at a uniform velocity v, the constant resistance body does not move in the initial stage, and the deformation of the anchor cable is elastic deformation at this time, and the maximum displacement of the anchor cable is × 1 = P₀/k as the tension P increases. When P = P₀, the constant resistance body and the casing start to slip relatively, and then the constant resistance body oscillates inside the casing under the action of frictional and elastic forces (Gong et al. 2020). When the constant resistance body oscillation stops, the constant resistance body and the casing stop moving relative to each other, and the tension produced at this time is the smallest and is called the lower limit constant resistance P₁.

After the constant resistance body and casing stop relative movement, when the tension increases again as the constant resistance body moves again, the NPR anchor cable will repeatedly enter the sticking phase, a sticking phase within the displacement generated by \(\Delta x\), the formula is:

The relationship between the quasi-static tension load P and displacement x can be derived from Eq. (4), i.e., the mechanical principal equation of the NPR anchor cable:

The intrinsic structure curve of the NPR anchor cable under static load (Tao et al. 2021a, b) can be further obtained according to Eq. (5), as shown in Fig. 7.

Schematic diagram of constitutive relation of NPR anchor cable

3.2 Experimental analysis of NPR anchor cable mechanics

The experiments were carried out using HWL-2000 constant resistance large deformation anchor cable tension test system and HZ-200000 J constant resistance large deformation anchor cable drop hammer impact test system for static tension and dynamic impact experiments, respectively (Wang et al. 2021; Tao et al. 2022a, b). The specification of constant resistance casing is φ133 × 2000, the specification of constant resistance body is φ93 ~ φ95, and the length of anchor cable is 2.5 m.

From the static tension curve Fig. 8a, it can be seen that: When the tensile displacement of NPR anchor cable is about 200 mm, NPR anchor cable starts to show constant resistance phenomenon, at this time the force value of anchor cable is above 300 kN, the average is about 350 kN. and fluctuates continuously around this value before the anchor cable is damaged, and the final slip distance is about 800 mm, showing a good constant resistance effect.

NPR anchor cable mechanics experiment

From the power shock curve, Fig. 8b, it can be seen that: The maximum impact resistance of NPR anchor cable during the power impact is about 210 kN. The deformation of NPR anchor cable during impact is divided into 3 stages: plastic deformation stage, elasto-plastic deformation stage and elastic deformation stage. A large value of shock resistance from 0 to 29 ms, which keeps fluctuating. A small vibration started at 29 ms ~ 36 ms with a downward trend. The fracture of the anchor cable starts at 36 ms by the impact until it drops to 0 at 45 ms.

According to the rock mechanics experiment of Minxian tunnel, a FLAC3D numerical simulation model with length, width and height of 50 m × 20 m × 50 m was set up to simulate the tunnel excavation site with burial depth of 200 m, horizontal stress of 6.3 MPa and applied stress of 3.5 MPa at the top of the model. The model mainly uses the combination of long (12 m) and short (7 m) NPR anchor cables to control the deformation of surrounding rock, and the inter-row distances are 2000 mm × 600 mm and 1000 mm × 600 mm respectively to mobilize the stable rock mass in the deeper part. The specific distribution of anchor cables is shown in Fig. 9, and the mechanical parameters of rock and anchor cables are shown in Tables 3 and 4.

Comparison of numerical simulation and physical model experiment

4.1 Numerical simulation of rock movement under unsupported condition

As shown in Fig. 10, during the excavation of the upper platform, the maximum settlement displacement of the tunnel surrounding rock occurs at the top of the arch position, which is 0.66 m, and the phenomenon of falling blocks occurs at the top of the palace position at this time, and the displacement of the arch shoulder position is about 0.58 m, which shows a large number of fissure development phenomenon; The maximum displacement of the surrounding rock is about 0.78 m during the excavation of the middle step, at which time the top slab rises and the arch shoulder fissure zone is further developed and accompanied by a small amount of rock spalling; The maximum settlement displacement during the excavation of the lower step is about 0.94 m, at which time the floor bulge is further developed and a large area of the vault top appears to fall off the block; When the maximum settlement displacement is about 0.84 m when the elevated arch is excavated, the upper and lower slabs are collapsing and collapsing, and the surrounding rocks on both sides are further cracked and fallen, and the tunnel surrounding rocks are seriously damaged.

Comparison of numerical simulation without support

4.2 Numerical simulation of the surrounding rock movement under NPR anchor cable support condition

The numerical simulation clouds of displacement and pressure in the NPR anchor cable support state are shown in Figs. 11 and 12. It can be seen from the Figs. 11 and 12 that the NPR anchor cable has a strong restraining effect on the tunnel surrounding rock. The maximum settlement displacement after excavation of the full section is 0.078 m and the maximum pressure is about 1.4 MPa, which has an obvious control effect and proves that the NPR anchor cable has a super strong compensating mechanical effect. The specific analysis is as follows:

Comparison of numerical simulation displacement under NPR support condition

Stress cloud image display

From Figs. 13 and 14 it can be seen that the surrounding rock in the arch area of the tunnel mostly shows a settlement trend, while the bottom area shows an uplift trend. When excavating from the upper to the lower step, the settlement value of the tunnel surrounding rock shows a trend of increasing, the maximum to 0.14 m, while the maximum settlement displacement is about 0.078 m under the support of NPR anchor cable after the excavation of the elevation arch, because the elevation arch has the function of closing the surrounding rock and improving the overall bearing capacity of the surrounding rock. During the excavation of the tunnel as a whole, the vertical stress is dominated by pressure, and the maximum pressure in the arch area is about 0.7 MPa. From the physical model DIC monitoring map, it can be seen that the displacement interval of the tunnel surrounding rock under NPR anchor cable support ranges from 1.2 mm to 2.7 mm, and the displacement settlement value is small. The overall displacement under NPR anchor cable support is below 300 mm, which proves that NPR anchor cable is effective in supporting large deformation tunnel in soft rock.

NPR anchor cable support scheme of Minxian tunnel

Tunnel monitoring diagram

Based on the above study, it is known that the surrounding rock of Minxian tunnel is severely broken and belongs to soft rock large deformation tunnel, therefore, ordinary support can not support the deformation damage of surrounding rock. Through numerical simulation experimental research it is known that NPR anchor can be effective in supporting the surrounding rock of Minxian tunnel. In order to more accurately prove the compensatory mechanics of NPR anchor support effect, a combination of long and short NPR anchor support scheme is designed for Minxian tunnel, and the specific support design is shown in Fig. 13.

As shown in Fig. 14, monitoring points are set in the NPR support section of the tunnel, so as to monitor the displacement and stress curve changes of the tunnel surrounding rock under the NPR anchor cable support conditions, where the monitoring points are the top of the vault, the left and right arch shoulders and the left and right arch waist of the section. The initial support pressure is monitored by YL-ESG earth pressure box produced by Shanghai Rocklink as the stress monitoring element. The earth pressure box is welded to the back of the steel arch in the initial pressure, and for the second lining perimeter pressure, the earth pressure box is first welded to the steel pallet, and then the steel pallet is welded to the perimeter of the reinforced concrete lining's steel mesh mold. When the surrounding rock is deformed, the deformation pressure can be transferred to the anchor cable constant resistance body through the force gauge.

As shown in Fig. 15, the field monitoring of the surrounding rock displacement, initial support pressure, second lining pressure and NPR anchor cable axial force gauge curve after NPR anchor cable support is shown. As shown in Fig. 15a, the deformation of the surrounding rock after the NPR anchor cable support is greatly reduced, and the maximum displacement produced by the vault is about 74 mm. The anchoring mechanism of the NPR anchor cable is more shear-resistant than mobilizing the deep stabilized surrounding rock. As shown in Fig. 15b, the contact stress between the initial support and the surrounding rock is reduced compared to the original support condition. The initial support stresses in the monitored sections were 0.14 MPa, 0.11 MPa, 0.07 MPa, 0.06 MPa and 0.03 MPa, respectively. The deformation of the surrounding rock was significantly reduced by the NPR anchor cable, and the deformation of the surrounding rock was significantly controlled. The distribution law of the second liner pressure and the distribution law of the surrounding rock deformation in this section are still basically consistent. As shown in Fig. 15d, the preload force of the NPR anchor cable is about 310 kN. The high preload force provides a high radial constraint force for the surrounding rock in time, which reduces the stress adjustment amplitude of the surrounding rock and limits the development of the loosening circle in the surrounding rock.

Field monitoring curve

The indoor experiment shows that NPR anchor cable has a super-strong constant resistance effect, the elongation can reach 800 mm and the constant resistance value is maintained above 300 kN, which proves that the indoor experiment effect of NPR anchor cable is good, and then the support effect of NPR anchor cable is further verified by numerical simulation and field experiment. Through numerical simulation and on-site support experiment, it can be seen that the maximum tunnel displacement settlement under NPR anchor cable support is 47 mm and 74 mm respectively, both of which are below 300 mm, which proves that NPR anchor cable has a good supporting effect on soft rock tunnel with large deformation. Specific experimental conclusions are as follows:

1. (1)

   According to the ground stress characteristics of Minxian tunnel and the surrounding rock strength measurement, it is concluded that the surrounding rock strength of Minxian tunnel is low, joints and fissures are developed, the rock body shows serious fragmentation, and the maximum main stress value of the tunnel is 6.308 MPa at a burial depth of 200 m. Therefore, Minxian tunnel is a high stress soft rock tunnel with high support requirements.

2. (2)

   According to the analysis of numerical simulation experiment, the maximum convergence of tunnel surrounding rock after NPR anchor cable support is 0.078 m, and the maximum pressure is about 1.4 MPa. It proves that the NPR anchor cable has super mechanical support effect on the high stress soft rock tunnel.

3. (3)

   The field monitoring curve after NPR anchor cable support shows that the maximum settlement displacement of the tunnel in the experimental section is about 74 mm, which is similar to the numerical simulation results, and the constant resistance value of NPR anchor cable is maintained at about 310 kN, which proves that NPR anchor cable has a super strong mechanical compensation mechanism and is effective in supporting the tunnel with large deformation of soft rock.