1 Introduction

Bolt support is one of the main and common methods to control the stability of tunnel surrounding rock (Kang et al. 2010). However, due to the imperfection of anchoring mechanism, there are some safety problems in the engineering application of bolt support (Lu et al. 1998).

At present, the mechanism of tunnel anchoring mainly includes the mechanical mechanism of interaction between surrounding rock and supporting structure, and the mechanical mechanism of overall anchoring surrounding rock structure. The interaction theory of rock bolt and surrounding rock considers the relative displacement of rock bolt and surrounding rock, and reflects the effect of progressive failure of surrounding rock on the rock bolt structure. The mechanical mechanism of the whole anchoring surrounding rock structure considers that the supporting rock mass and the supporting structure form a completed new structure, which ensures the safety and durability of the tunnel.

Zhou et al. (2016a, b), Liu et al. (2017), Chen et al. (2018). analyzed the mechanical mechanism of load transfer between bolt and surrounding rock according to the idea of interaction between bolt and surrounding rock, obtained the distribution characteristics of axial stress and interfacial friction resistance of bolt, and proposed the calculation method of anchoring design parameters, which were applied in a large number of projects. Xie et al. (2015), Wen et al. (2015), Li et al. (2015). constructed the mechanical model of composite supporting structure and put forward the theory of composite supporting structure of soft rock tunnel according to the mechanical characteristics of interaction between surrounding rock and bolt.

The study shows that the interaction theory can solve the practical engineering problems well in the case of intact surrounding rock or small breaking degree and breaking range of surrounding rock (Wang et al. 2019). However, when the fracture degree of tunnel surrounding rock is high and the broken range is large, the interaction theory cannot play a guiding role in the design of bolt support, and tunnel safety accidents caused by improper design often occur (Cai et al. 2004).

When the broken area of tunnel is large, it is difficult to control the stability of tunnel by using conventional unprestressed system bolt, the main reason is that installing this kind of bolt cannot realize the mutual restraint between the broken rock blocks, and the broken rock cannot form an organic whole resisting the load (Chen et al. 2011; Li et al. 2013).

In order to understand and master the mechanical law and mechanism of the stability control of the tunnel with broken surrounding rock by prestressed bolt, researchers at home and abroad have carried out in-depth research on this problem. From June to July 2020, China National Coal Mining Research Institute conducted model tests using the first self-developed “similar simulation test rig for bolt support in large-proportion roadway” (http://tdht.ccteg.cn/contents/4004/21370.html) .For the first time, the strengthening effect of bolt support on broken rock mass is studied quantitatively, which verifies that the high prestressed bolt support can form the supporting stress field in rock mass, significantly improves the integrity and bearing capacity of rock mass, and further reveals the mechanism of bolt support..

Experiments show that the bolt pre-tightening force can increase of confining pressure of rock mass, change the stress state of surrounding rock effectively, improve the mechanical properties of the anchored rock mass, increase the anchoring strength of rock mass and, in turn, increase the bearing capacity of the surrounding rock, control and reduce the tunnel surrounding rock broken zone, plastic zone and the surface displacement of the tunnel, which is helpful to maintain the stability of surrounding rock (Zhu 2011).

In recent years, domestic scholars put forward the integral structure theory of tunnel anchorage on the basis of the experimental study of rock anchorage. The basic principle is to make use of the extrusion action of prestressed anchoring rob to form the whole anchoring structure with certain bearing capacity in the broken surrounding rock of the tunnel, and rely on this bearing structure to control the in-situ stress of the tunnel and realize the control of the tunnel stability (Liu et al. 2013, Guo and Yang 2008).

Although interaction theory and integral structure theory have been widely used in practical engineering, there are still some shortcomings. Firstly, the interaction theory and the whole structure theory are summarized and analyzed in this paper. According to the synergistic theory of tunnel anchorage, an improved synergistic theory—I·L·4S is proposed. The correctness of the proposed theory is verified by analyzing the deformation and internal forces of bolt and lining in the model test.

2 Synergy Theory of Tunnel Anchorage System

The deformation and failure of tunnel surrounding rock are obviously gradual and periodic. Tunnel construction breaks the original equilibrium state of rock mass, and the disturbed rock mass deforms in the excavation face in order to seek a new balance. When it cannot balance itself, tunnel support is needed. The essence of tunnel support is to "mobilize" and "assist" surrounding rock bearing, that is, to bear the additional load of surrounding rock caused by construction.

The periodic characteristics of the gradual failure of the surrounding rock and the dynamic development phenomenon of the pressure arch indicate that the deformation and failure of surrounding rock are grouped. As a natural geological material, the time-efficiency of stress transfer and displacement release of surrounding rock and the structure of strata material determine the grouping characteristics of deep surrounding rock, and each group of deep surrounding rock is almost simultaneously unstable. Under long-term geological action, the mechanical properties and stability of the rock strata close to the inner side of the tunnel are generally better than that of the outer side. Therefore, the inner wall rock with a certain bearing capacity can be divided into structural layer, and the outer wall rock exists as a load body, which is called the load layer. Each group of deep surrounding rock consists of load layer and structural layer. The anchorage system has the dual function of mobilizing and assisting the surrounding rock to bear the load. It not only fully mobilizes the self-bearing capacity of the surrounding rock, but also assists the surrounding rock to bear part of the load that it cannot bear by itself, so as to realize the joint bearing with the surrounding rock, thus enhancing the stability of the surrounding rock.

Although the system bolt can form the structural layer and load layer together with the surrounding rock mass to realize the supporting function of the tunnel, However, for some large-span tunnels or soft-rock large-section tunnels, such support structure cannot completely control the deformation of surrounding rock and support structure, and cannot meet the needs of tunnel surrounding rock stability. Therefore, it is often necessary to form a new support structure system of system bolt + long anchor cable + surrounding rock mass. Various support units work together to maintain the stability of the tunnel.

On the basis of the above ideas, Professor Zhang Ding-li (Sun et al. 2019) proposed the synergistic effect theory of anchorage system. In his view, tunnel anchoring system is a complex system composed of surrounding rock, rockbolt, anchoring cable and other anchoring structures in a certain working mode, which is in a dynamic equilibrium state through organic connection with external strata and engineering environment. The stability of the anchoring system is the result of the interaction between the subsystems, which is mainly affected by the properties of the anchoring material, the quality of the surrounding rock and the properties of the anchoring rock. The synergistic effect of the anchoring system includes three aspects: the interaction between the anchoring system and the compound surrounding rock structure, the matching effect among the parameters of the single supporting type of bolt or anchoring cable, and the synergistic effect between the bolt and anchoring cable. The synergistic structural model is shown in Fig. 1.

Fig. 1
figure 1

Synergistic mechanism of anchoring system (Sun et al. 2019)

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By analyzing the force situation of the anchorage system in Fig. 1, Professor Zhang believes that the core of bolt support is to form the whole surrounding rock structure through the composite beam or compression arch effect, and the anchoring cable suspends the structure to the stable rock layer to bear the self-weight load and the deformation load transferred to the anchor cable due to the further deformation of the surrounding rock. The two synergistic effects mobilize the bearing capacity of the deep surrounding rock. Through the synergistic effect between the anchoring system and surrounding rock, the deformation of the anchoring system can be coordinated, and the load distribution of surrounding rock can be matched with the supporting performance, so that the deformation of surrounding rock can be controlled scientifically and reasonably.

Based on the structural model, Zhang further proposed four mechanical models of support structure under different working conditions, as shown in Fig. 2.

Fig. 2
figure 2

Mechanical model for synergy of anchoring system (Sun et al. 2019). a Working condition a. b Working condition b. c Working condition c. d Working condition d

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By analyzing the four mechanical models in Fig. 2, the conclusion can be drawn as follows: the essence of failure of the anchorage system is that the anchor cable is subjected to excessive force due to the excessive deformation of the overall structure of the bolt-surrounding rock. It can be seen that the necessary condition for the instability of the anchor system is the failure of the anchor cable. Combined with the action mechanism of the anchor system, the supporting performance of the anchor bolt should be fully utilized in the anchor system, and the anchor cable should have enough redundancy when it carrying capacity is large. Because the synergistic effect of tunnel anchorage system is aimed at controlling the stability of surrounding rock, and the deformation of surrounding rock can not only reflect the development status of compound surrounding rock structure, but also have a certain correlation with the load effect, so it can be used as the judging basis of surrounding rock stability and the evaluation index of the synergistic effect.

3 The Improved Synergy Theory of Tunnel Anchorage System and Its Experimental Model Verification

After the synergistic theory of tunnel anchoring system was proposed, the author of this article has made some improvements to it, and obtained the synergistic mechanical mechanism of the new anchoring system, which is composed of the system of compressive anchor bolt + tunnel lining + supporting surrounding rock, and has been verified in the laboratory model test.

The phenomenon of zonal disintegration is a special form of surrounding rock failure in deep tunnel. On the basis of previous studies, I have made an in-depth study of it (Wang et al. 2018). Research results show that deep buried tunnel under the larger axial stress, deformation of tunnel surrounding rock will expand and deform towards the cavern space, At this time, the surrounding rock near the tunnel wall will produce radial tensile stress, when the stress value reaches limit stress of surrounding rock, it will produce tensile rupture, that is, the first layer of fracture zone will appear, which is equivalent to forming a larger tunnel on the original foundation when the axial stress of the tunnel continues to increase, a new fracture zone will occur. When the original rock stress outside the surrounding rock of the zonal disintegration reaches the initial stress state again, the zonal disintegration stops.

In order to deeply study the mechanical mechanism of high-strength yielding bolt support and lining and surrounding rock collaborative anchorage of deep buried and zonal disintegration tunnel (Zhu et al. 2018), the engineering test results and model test results were compared and analyzed, and concluded that the occurrence of zonal disintegration was mainly caused by tension and compression alternation in surrounding rock strain region under the action of large axial stress in deep buried tunnel, while bolt support may have On this basis, the distribution characteristics of the axial stress and interface friction resistance of the bolt are obtained by establishing the mechanical model of the interaction between the bolt and the surrounding rock: the axial stress of the bolt reaches the peak value in the split ring and forms multiple peaks along the bolt direction; the interfacial friction resistance of the bolt will form tensile stress within a certain range of the anchor head, and form a tensile stress at the end of the bolt. The compressive stress is formed in a certain range. Therefore, the supporting mechanism of bolt support is that the cooperative effect of anchor head and surrounding rock in the deep pressure (pressure strain) region of surrounding rock presents the locking effect of embedding and occlusion, and the synergistic effect of bolt tail and surrounding rock presents suspension effect, thus the bolt, lining and surrounding rock form a relatively stable self-supporting arch, which plays a supporting role. The appearance of self-supporting arches has caused the bolt and rock mass to be compressed. Therefore, the mechanism of the bolt is Insert + Lock + Stretch + Self-Bearing + Support + Squeeze, referred to as I·L·4S.

In order to verify the correctness of the theory, the author carried out the corresponding model test (Chen et al. 2019). The model test was carried out on the geological disaster simulation test platform of Dalian University, and the size of the test model was 3 × 3 × 3. The rock mass in the test was calculated according to the similarity principle, and the basic size of the surrounding rock of the deep buried tunnel was obtained. In the test model, the supporting structure of the tunnel is composed of high-strength yielding system bolt and lining with different stiffness, and the bolt penetrates into the fractured surrounding rock of tunnel zone. The stress sensor and strain brick are embedded in the model to test the internal force and deformation of surrounding rock and supporting structure. After half a year's monitoring, the strain characteristic curves of lining and anchor are obtained.

The test results show that the high-strength yielding bolt support has obvious effect on eliminating or reducing the zonal fracture. The test and model test results show that the surrounding rock zonal fracture basically disappears after the high-strength yielding bolt support, and the overall stability of the tunnel is improved. The results show that the axial force of the bolt in the zone broken surrounding rock gets the corresponding peak value near the zone fracture ring, forming multiple peak continuous states as a whole; the friction resistance or interfacial shear stress of the bolt presents tension and compression state, that is, the compressive stress in the space near the tunnel and the tensile stress in the anchor head.

According to Fig. 3, the stress characteristics of the bolt can be obtained. The rock mass behind the support structure has always been in the active stress state, and the emergence of excavation space leads to the disappearance of the passive stress on the support structure, which makes the stress of the support structure point to the tunnel space. Therefore, the tunnel surrounding rock inevitably produces tensile deformation pointing to the tunnel. Although the bolt has been in the action state, through observation, the safety effect of the tunnel with flexible lining and bolt support is not as good as that of the tunnel with rigid lining and bolt support. Although there is no or weaken the zonal disintegration phenomenon, the surrounding rock deformation of the tunnel with flexible support composite structure is larger, and it appears certain large deformation under the continuous loading state. The reason for this kind of deformation is that the flexible lining cannot provide high support force, which leads to the flexible lining exerting the characteristics of coupling deformation with surrounding rock to ensure the stability of tunnel under the action of high unloading stress. The stress state of bolt at this time is that the surrounding rock of tunnel is always in tensile state the bolt is also in tension. Therefore, in order to determine the safety of the tunnel by monitoring the stress of the bolt, it is necessary to comprehensively determine the safety of the tunnel by monitoring the deformation of the lining and surrounding rock.

Fig. 3
figure 3

The Strain measurement results of No. 1–5 measuring points of pressure-relief anchors with the excavation steps on difference point

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On the premise of observing and analyzing the force of bolt and other supporting structures, the deformation of surrounding rock is measured in the test. The calculation results of numerical simulation and test results of physical model test are shown in Table 1. The numerical calculation results are derived from the numerical simulation, and the numerical calculation model is established according to the physical test model, and the finite element method is used to calculate. The elastoplastic continuum element is used to simulate the surrounding rock mass, and the elastic structural element is used to simulate the supporting structure. Please read the references for details (Chen et al. 2019).

Table 1 Numerical simulation and physical test results of different working conditions
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By comparing the displacement and strain results of tunnel surrounding rock from Figs. 4 and 5, the strain and displacement curves of the tunnel surrounding rock under all supporting conditions show wave changes in peaks and troughs, rather than traditional failure rules. It is indicated that the tunnel still has zonal disintegration phenomena and trends under the support results. The numerical calculation results are basically consistent with the test results.

Fig. 4
figure 4

Displacement curve diagram of numerical model of various working conditions

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Fig. 5
figure 5

Strain curve diagram of numerical model of various working conditions

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By comparing the displacement and strain results of surrounding rock under different supporting conditions, it was obtained that under the combined support structure of rigid lining and yielding bolt, the zonal disintegration trend of wave variation of displacement and strain curve is obviously weakened, which indicates that the yielding structure can not only restrain the zonal disintegration of surrounding rock, but also weaken the zonal disintegration trend of surrounding rock.

The analysis shows that the rock around the tunnel forms an anchorage mass and connects with the stable rock mass in the distance due to the addition of yielding bolt, which makes the stress field of surrounding rock more uniform, and the strain and displacement of rock mass around the tunnel are relatively reduced, thus restraining the zonal disintegration trend of surrounding rock. At the same time, the yielding performance of the yielding bolt is equivalent to increasing the support strength of the supporting structure, reducing the rock fracture around the tunnel and maintaining the stability of the surrounding rock.

In order to study the role of lining supporting structure in the deformation of surrounding rock and the supporting effect of yielding anchor on lining, the numerical calculation results of lining bending moment and strain at roof, arch shoulder and side wall in various supporting conditions are selected for comparative analysis and research. The lining bending moment and strain values are shown in Table 2.

Table 2 Numerical simulation of different lining working conditions
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By analyzing the internal forces of the roof, arch shoulder and side wall of the lining support structure in each supporting condition, it can be seen that the bending moment and strain of the supporting structure are the largest, which indicates that the deformation of the surrounding rock at the roof and side wall of the tunnel support structure is the largest, which is in good agreement with the actual observation results.

Comparing the internal forces of roof, spandrel and side wall of lining support structure in various supporting conditions, it was shown that the strain value of side wall and roof of supporting structure is the largest, which indicates that the elastic resistance of lining roof and side wall is larger and the stability is lower. The bending moment and strain of combined support structure with lining support and yielding bolt is significantly reduced than that of single lining support structure the elastic resistance of the lining roof and side wall is reduced and the stability is improved.

It is considered that the rock surrounding the tunnel will form a more stable anchorage body after the yielding anchor was added. The relatively stable anchorage body realizes the transfer and redistribution of stress, makes the stress field around the tunnel more uniform, weakens the zonal disintegration trend of surrounding rock, and achieves better supporting effect.

By analyzing the mechanical mechanism of yielding structure, it can be seen that the anchoring mechanism of yielding structure is to form an effective anchorage mass in its support range and connect with the stable surrounding rock in the distance, which expands the bearing circle of surrounding rock, realizes the stress transfer, changes the stress state of surrounding rock, and suppresses the trend of zonal disintegration. At the same time, according to the composite arch theory, the yield distance can improve the support strength of the support structure and maintain the stability of the surrounding rock of the tunnel.

In summary, the synergistic effect of the new type of combined support structure of rigid lining and yielding bolt support system and surrounding rock can effectively suppress the zonal disintegration of deep-buried surrounding rock and at the same time reduce its tendency to rupture. The arrangement of the supporting structure has a good supporting effect on the stability of the surrounding rock of the deep-buried roadway.

4 Conclusion

The supporting structure of tunnel surrounding rock is a very complex composite structure. According to the cooperative action principle of tunnel anchorage system, the author summarizes his research results, improves and puts forward the I·L·4S theory. The main conclusions are as follows:

  1. 1.

    The surrounding rock of tunnel is composed of shallow surrounding rock with poor internal stability and deep surrounding rock with strong outer bearing capacity. On the one hand, anchoring system provides radial binding force for shallow surrounding rock, and transfers additional load of shallow surrounding rock to deep surrounding rock to mobilize surrounding rock bearing capacity; on the other hand, it forms certain arch effect around the tunnel to assist surrounding rock load.

  2. 2.

    The core of the coordinated action of anchoring system is to form a whole structure through bolt, lining and surrounding rock, and at the same time, the suspension effect of bolt can mobilize the bearing capacity of deep surrounding rock. Its connotation includes the interaction between anchorage system and composite surrounding rock structure, parameter matching of single support type of bolt, and synergy between bolt and lining. Its essence is deformation coordination and surrounding rock load Reasonable distribution.

  3. 3.

    The mechanism of anchor bolts in the support of deep-buried tunnels in zonal disintegration surrounding rock can be expressed as the interplay between the anchor bolt head in the deep pressure (compressive strain) area of the surrounding rock and the surrounding rock shows the locking effect of embedment and occlusion. The synergistic effect of the rod tail and the surrounding rock presents a suspension effect, while the bolt and the supporting surrounding rock as a whole form a relatively stable self-supporting arch, which plays a supporting role. The appearance of self-supporting arches has caused the anchor rod and rock mass to be compressed. Therefore, the mechanism of the anchor rod is Insert + Lock + Stretch + Self-bearing + Support + Squeeze, referred to as I·L·4S.

  4. 4.

    The results show that the axial force of the bolt in the zonal disintegration surrounding rock gets the corresponding peak value near the zonal disintegration ring and forms multiple peak continuous states as a whole; the friction resistance or interfacial shear stress of the bolt presents tension and compression state, that is, the compressive stress in the space near the tunnel and the tensile stress in the range of the anchor head. The results of field measurement and model test show that the zonal disintegration of surrounding rock is basically disappeared after bolt support, and the overall stability of tunnel is improved.