1 Introduction

In recent decades, rapid economic growth in China has resulted in significant increases in passenger and freight transport volumes, triggering widespread construction of nationwide transportation infrastructures, such as bridges, subgrades, and tunnels [1,2,3,4]. One specific concern is that existing small-to-medium-span tunnels are insufficient to satisfy escalating traffic demands. Consequently, an increasing number of large-span and super-large-span tunnels are being constructed to accommodate multiple traffic lines [5, 6]. Herein, tunnels with spans greater than 12 m are considered large-span tunnels, whereas super-large-span tunnels are characterized by spans exceeding 14 m, as specified by the Chinese Code for Design of Railway Tunnel [7]. However, the construction of large-span tunnels poses specific challenges such as the potential collapse of surrounding rocks [8], which has also been observed in similar tunnel projects worldwide [9, 10].

A primary factor contributing to the challenges in large-span tunnel construction is the low height-to-span ratio [11, 12]. Previous research has demonstrated that large-span tunnels exhibit extensive disturbance zones, leading to complex mechanical behaviors and reduced self-stability of the surrounding rock mass [13, 14]. These challenges are magnified when tunnels are excavated in soft rock strata because of the weak properties and creep behavior of the rock mass [15,16,17]. Engineering experience and numerical studies have revealed that tunnel deformation and rock mass pressure are significantly affected by construction processes and support systems [18,19,20], thus highlighting the necessity of employing appropriate excavation procedures and support schemes for the successful completion of large-span tunnel projects.

When selecting an excavation procedure, factors such as safety, construction rate, operability, economic cost, and environmental impact should be comprehensively evaluated and compared [21, 22]. Currently, the sequential excavation method, which divides the excavation into several parts and tends to be more effective for stability control, is adopted in tunnel projects worldwide. This method can be classified into various categories based on the detailed excavation procedures. Numerous numerical and case studies have been conducted to investigate the viability of these diverse categories and their respective impacts on the mechanical behaviors of surrounding rock mass and the tunnel support systems [23, 24]. For instance, Yoo [25] conducted 3D numerical investigations to assess the performance of a sequential excavation method in soft rock tunneling. Williams et al. [26] examined two tunnel excavation cases in the northeast line of Singapore that employed the three-bench excavation method combined with wet-sprayed concrete. In the context of tunnel construction involving squeezing rocks, Liu et al. [1] conducted a case study to investigate the effects of a triple-bench annular excavation method using reserved core soil. Concerning soft rock tunnel excavation, Luo et al. [27] studied the mechanical responses of the surrounding rock mass and tunnel linings during the construction of the large-span triple-arch tunnel at Badaling Great Wall station. Overall, the sequential excavation method has gained widespread recognition owing to its ability to enhance tunnel face stability.

Notably, the sequential excavation method typically necessitates a significant deployment of internal temporary supports to partition the tunnel face and support the rock mass. However, internal supports suffer from some limitations, such as (i) obstructing the utilization of large-scale excavation equipment, thereby reducing the construction rate [28, 29]; (ii) necessitating multiple stages of internal support installation and removal during excavation, thus complicating the construction process [30, 31]; and (iii) the subsequent removal of internal supports, which can lead to a conversion of the support structure’s force system, potentially endangering structural safety [23, 32]. Considering these limitations, efforts should be made to achieve an enhanced balance between construction safety and efficiency.

One way to overcome these limitations is to install prestressed anchor cables outside the initial support as an alternative to the conventional construction of an internal support. Previous studies demonstrated that this innovative support system can play a role similar to that of internal steel supports in stabilizing the surrounding rock [33, 34]. However, field experience using prestressed anchor cables to replace the “burdensome” internal supports in super-large-span soft rock tunnel projects remains limited. To this end, this study adopts the “Shed-frame” principle and corresponding field data to explore the feasibility of using prestressed anchor cables as an alternative to internal temporary supports during super-large-span tunnel excavation in soft rock masses. Specifically, a station tunnel section in Wumengshan Tunnel No. 2 was selected as a representative example, with extensive monitoring data collected and analyzed to study the deformation characteristics of the surrounding rock mass and the mechanical behavior of the support system. The findings and discussion, which may provide valuable insights for popularizing and developing the proposed support system, are summarized at the end of the paper.

2 Project overview

2.1 Engineering background

The Guiyang–Kunming Railway, connecting the Guizhou and Yunnan provinces, is one of the main railways in southern China. Wumengshan Tunnel No. 2 is part of the Guiyang–Kunming Railway, as depicted in Fig. 1. A 538-m-long four-line railway station tunnel section runs from mileage DK287 + 812 to DK288 + 350, as shown in Fig. 2. Notably, the station tunnel section has a typical super-large span of 24 m. The surrounding rock masses within the station tunnel section are limestone, mudstone interbedded with limestone, and mudstone—rated as Type IV or V according to the rock mass rating (RMR) method [35]. The rock mass exhibited an uneven hardness distribution within its composition and was characterized by considerable fragmentation. Mudstone exhibits weak mechanical properties and is susceptible to weathering. The limestone displays a high degree of rock hardness, accompanied by intense karst development.

Fig. 1
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Geographic location of the Wumengshan Tunnel No. 2 (adapted from Google Earth)

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Fig. 2
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Geology profile along the tunnel axis

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2.2 Support system

As presented in the schematic of Fig. 3a, b, the traditional support system consists of a pipe shed and the frame scheme. More precisely, the internal and initial supports merge to form a comprehensive framework in conjunction with the shed, creating a “shed-frame” system [36]. In this configuration, excavation-induced earth pressures are conveyed through micro-arches between the pipes, exerting force upon the system [37, 38]. Such an arrangement facilitates a collaborative response of the system to control and withstand the released pressures effectively. In contrast, as shown in Fig. 3c–d, the presented innovative support system incorporates prestressed anchor cables. These cables eliminate the need for the “burdensome” internal supports while simultaneously integrating the initial support with the shed, thereby also forming a “shed-frame” system, designed for collaborative functionality.

Fig. 3
figure 3

Schematic of the “shed-frame” system: a the traditional support system featuring internal support; b the presented support system featuring prestressed anchor cable. The symbol F stands for forces applied by the internal supports or prestressed anchor cables on the tunnel

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Regarding the presented case, a representative profile is shown in Fig. 4a. Typically, the span of the tunnel is 24.0 m and the height is 16.8 m. Traditional "shed-frame" system demand a significant deployment of internal supports, as depicted by the dashed lines in Fig. 4b. In contrast, the objective of the support system design in this project was to replace the internal temporary supports with prestressed anchor cables. Notably, a constrained number of supports are still in use, as indicated by the yellow shading in Fig. 4b. This retention arises from the necessity of maintaining a functioning and comprehensive framework immediately after excavating the two drifts (labeled I and II in Fig. 4a)—necessary because the construction of prestressed anchor cables is extremely time-consuming, as it includes cable installation, grouting, and subsequent anchor cable tensioning, which typically requires seven days. Thus, to ensure construction safety, a small number of supports are retained but intended to be removed before the excavation of the middle bench. Overall, the use of temporary internal supports was considerably reduced.

Fig. 4
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Cross section of the station tunnel section: a detailed dimensions of the tunnel face; b comparison of the support system between traditional methods and the method employed in this project; c detailed designs of the support system

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A detailed design of the support system is presented in Fig. 4c. The designs for the pipe shed and initial support were informed by extensive engineering experience. However, expertise in designing prestressed anchor cables within the context of tunnel engineering remains limited. Consequently, the design of the prestressed anchor cables considered the following methodology.

Initially, the removal of internal supports prior to the excavation of the middle bench was identified as a crucial checkpoint. From the perspective of construction safety, it is imperative that the vertical prestressed anchor cables (i.e., A1, A2, B1, and B2 in Fig. 4c) possess adequate capacity to withstand the entirety of rock pressures exerted on the support system. This necessity arose in that, at this stage, the removal of the internal support left the framework incomplete and potentially ineffective.

Subsequent to this checkpoint, the design intentionally exploits the synergistic effect of the “shed-frame” system, drawing on the cooperative functionality of all components to withstand the pressures. This strategy is underpinned by the fact that, during the excavation of lower benches, the horizontal prestressed anchor cables (say D1, D2, E1 and E2 in Fig. 4c) function akin to horizontal internal supports, thus rendering the framework completed and fully operational. Consequently, following the removal of the internal supports, a primary focus of the design is to ensure the cables have fixed anchor ends. Notably, to accommodate unforeseen uncertainties and potential inadequacies, this methodology is further enhanced by the integration of construction information technology. Specifically, in scenarios where the design proves insufficient and deformations exceed predetermined thresholds, an immediate emergency response, including the reinstatement of internal supports, can be implemented to mitigate any potential risks efficiently.

Regarding the above-mentioned checkpoint, the Protodyakonov’s equilibrium arch theory was employed to estimate the earth pressures exerted on the system. As shown in Fig. 5, the excavation process induces an arch-shaped disturbance zone above the tunnel, wherein the gravity of the loosened rock acts as the primary source of pressure on the tunnel. According to Protodyakonov’s theory, the arch shape equation can be written as follows:

$$y = \frac{{2x(W_{1} - x)}}{{W_{1} f}},$$
(1)

where W1 is the span of the arch, and W1 = Bt+2Ht tan(θ), in which Bt and Ht denote the width and height of the excavation area, respectively, and θ = 45°‒φc/2, with φc indicating the calculated friction angle of the rock; and f is estimated as f = tan(φc) [39].

Fig. 5
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Schematic of the Protodyakonov’s equilibrium arch theory

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Moreover, Fig. 6 illustrates that the prestressed anchor cables, anchored between two adjacent steel frames, are arranged in a staggered pattern. Accordingly, the effective longitudinal spacing between these cables, Ll, is 1.2 m. For the checkpoint under consideration, the six vertical anchor cables (i.e., A1, A2, B1, and B2 in Fig. 4c) must possess the capacity to withstand the entirety of the gravity of the loosened rock G over a longitudinal length of Ll. The design bearing capacity of a prestressed anchor cable Nd can be calculated as

$$N_{{\text{d}}} = \frac{{K_{{\text{s}}} G}}{6} = \frac{{K_{{\text{s}}} }}{6}\int_{0}^{{W_{1} }} {\frac{{2\gamma x(W_{1} - x)L_{{\text{l}}} }}{{W_{1} f}}{\text{d}}x,}$$
(2)

where Ks is a safety factor, set at 1.5; γ is the bulk density of the surrounding rock mass. Based on geotechnical survey, γ and φc are taken as 20 kN/m3 and 50° for the mudstone, respectively, yielding an Nd of approximately 1041 kN. Accordingly, the prestress is strategically designed to be approximately 50% of Nd, set as 500 kN. Maintaining 50% of the design bearing capacity allows for a safety margin should the axial force provided by the prestress prove insufficient.

Fig. 6
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Layout of the prestressed anchor cables

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In addition, this design capacity requirement Nd can be met with four steel strands, each 15.2 mm in diameter and possessing a tensile strength of 1860 MPa, leading to an ultimate bearing capacity Nk calculated as 1348 kN. To facilitate optimal cooperation among the anchor cables, the ultimate anchoring force should match Nk, resulting in

$$f_{{{\text{mg}}}} \times {\uppi }D_{{{\text{pac}}}} L_{{\text{a}}} = N_{{\text{k}}},$$
(3)

where Dpac is the diameter of the anchor cable hole (115 mm as shown in Fig. 6); fmg is the design value of the bond strength between the anchor cable and the surrounding rock mass, taken as 0.4 MPa, according to the code [40]; La is the anchorage section length, thus calculated as 9.3 m and rounded up to 10 m for construction convenience. Given the height of arch estimated as 10.4 m (Eq. (1)) during the checkpoint, the total length of the anchor cables is designed to be 20 m, ensuring that the anchorage section remains entirely within the non-disturbance zone.

2.3 Excavation method

The station tunnel section was constructed using a modified three-bench excavation method featuring two drifts on the upper bench. The main excavation procedure is as follows.

  1. 1.

    Upper bench excavation: As shown in Fig. 7a, the two temporary drifts on the upper bench (I and II) were first excavated with the protection provided by the pipe sheds. Subsequently, the initial support and internal temporary support around the drift were constructed, followed by the installation and tensioning of the surrounding prestressed anchor cables. Upon completing the excavation of parts I and II, part III was excavated, along with the encircling of the initial support installation and anchor cable pre-tensioning (Fig. 7b). Before the middle bench excavation, the internal temporary support was removed, as shown in Fig. 7c.

  2. 2.

    Middle bench excavation: During middle bench excavation, there was a slight interval between the excavation of parts IV and V. For each part, shotcrete, reinforcement grid, and steel frame were implemented (Fig. 7c). Subsequently, anchor bolts surrounding the middle bench were installed, with shotcrete spraying performed until the prescribed shotcrete thickness was reached. Subsequently, prestressed anchor cables were installed in the middle of the bench.

  3. 3.

    Lower bench excavation: Once the prestressed anchor cables encircling the middle bench were tensioned to the designated values, excavation of the lower bench commenced. The excavation was divided into two parts, as shown in Fig. 7d. Part IV was excavated before Part V. Both the steel frames at the invert and the remaining parts of the sidewalls were constructed in this stage, followed by shotcrete spraying to the design thickness. Subsequently, the secondary lining was sequentially constructed, commencing at the invert and subsequently extending to the sidewalls and tunnel arch.

Fig. 7
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Main excavation procedures of the station tunnel section: a excavation of drifts I and II ; b excavation of part III; c excavation of the middle bench; d excavation of the lower bench

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Following the above-mentioned excavation procedure, the benefits of replacing the internal temporary support with prestressed anchor cables become apparent: (i) as shown in the on-site image in Fig. 7d, the working space is spacious, which facilitates the use of large-scale equipment, thereby enhancing construction efficiency; (ii) a significant reduction in the temporary support removal process is achieved; and (iii) the prestressed anchor cables can serve as components of the permanent tunnel structure, thereby further enhancing the structural safety during the operational phases. Regarding excavation efficiency, this study collates instances of tunnel excavations analogous in scale to the present case while employing a substantial amount of internal support. Owing to limitations in the availability of the excavation rate data, only two instances were considered for comparison. Table 1 presents a comparative analysis of the estimated excavation rates. Observationally, the present case reveals a higher excavation rate (201.6 m3/d) compared to the referenced cases, which utilized a traditional support system.

Table 1 Comparison of excavation efficiency in projects analogous in scale to the present case
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2.4 Field monitoring scheme

A monitoring section was established at mileage DK288 + 220 (shown in Fig. 2). This section employs various instruments to monitor aspects such as tunnel and rock deformations, surrounding rock pressure, steel frame stress, axial force of the anchor bolts, and axial force of the anchor cables. The detailed layout of the monitoring points is shown in Fig. 8. A comprehensive description of the instruments and their respective monitoring methodologies is presented in Table 2.

Fig. 8
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Layout of the monitoring points: a stress monitoring points layout; b deformation monitoring points layout

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Table 2 Monitoring instruments and methods
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Specifically, the vertical displacements at the tunnel arch were monitored using an automatic level, with measurements manually conducted at designated points (V1–V3). The horizontal convergences at the upper, middle, and lower benches (C3–C5), along with those in the two drifts (C1 and C2), were measured using convergence gauges. Displacement meters were used to assess the rock displacements along the upper tunnel side. Furthermore, the even distribution of pressure cells enabled the monitoring of the surrounding rock pressure on the tunnel crown and sidewalls. Strain gauges affixed to the steel frame provide insights into the stress state. Seven sets of stress gauges were used to monitor the axial forces acting on the anchor bolts. Seven force-measuring rings were used to monitor the axial force of the prestressed anchor cables. Notably, although this study focused on the mechanical behavior of the support system and surrounding rock, more comprehensive raw data are available in [43].

3 Deformation characteristics

3.1 Horizontal convergence

The development of the horizontal convergence at monitoring points C1 and C2 is shown in Fig. 9. Negative values signify inward convergence. During the excavation of the two drifts on the upper bench, the horizontal convergence at C1 and C2 exhibited an initial gradual increase, followed by a rapid convergence. The maximum horizontal convergences recorded at C1 and C2 were 21.6 mm and 16.1 mm, respectively. Following the removal of the temporary support, the monitoring activities at C1 and C2 were stopped. The displacements at C3 and C4 also initially increased at the start of the middle and lower bench excavations, eventually leading to rapid convergence. A similar convergence pattern was observed for C5.

Fig. 9
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Monitoring results of horizontal convergence. Notes: Roman numerals indicate the commencement of excavation for each respective part. The arrow between two Roman numerals signifies the time interval between the excavation surface of earlier bench/part reaching the monitoring section and the excavation surface of the subsequent bench/part reaching the monitoring section

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The highest horizontal convergence was observed at C4 at approximately 55 mm. The ratio of the maximum horizontal convergence to the tunnel span is approximately 0.23%, which falls within the threshold values of 0.19%–0.80% mandated by the standard set in Ref. [44], thus indicating the efficacy of the implemented “shed-frame” system in stabilizing horizontal deformation.

3.2 Vertical displacement

The development of the vertical displacement is presented in Fig. 10, with negative values indicating settlement. At monitoring points V1 and V2, the most significant growth in vertical displacement was caused by the excavation of the upper bench, measuring 45.3 mm and 32.2 mm, respectively. These values constituted approximately 54.3% and 43.8% of the final displacements at V1 and V2, respectively, suggesting that the upper bench excavation induced the most significant increase in the vertical displacement at the tunnel arch, with minimal impact from the lower bench excavation.

Fig. 10
figure 10

Monitoring results for vertical displacement at tunnel arch

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The maximum displacement, measuring approximately 81.0 mm, was observed at V1 throughout the excavation. The ratio of the maximum vertical displacement to the span is approximately 0.33%. Previous studies have suggested that this ratio can range from 0.20% to 1.50% for tunnel excavation in soft rocks [13, 24, 27]. This observation further substantiates the “shed-frame” system’s effective role in controlling tunnel deformations.

Upon analyzing the deformation trends presented in Figs. 9 and 10, tunnel deformation development exhibits a distinct “staircase-like” pattern, which is more evident in Fig. 11, where we examined similar representative instances of tunnels excavated in weak strata, characterized by a super-large span, but with traditional support systems. For a comprehensive comparative analysis, the deformations were normalized. Excavations incorporating traditional supports typically exhibit consistent gradual deformation progression. In contrast, this case utilizing prestressed anchor cables shows a pronounced “staircase-like” deformation pattern, characterized by an initial increase followed by rapid stabilization, attributed to the operational mechanism of the anchor cables. Unlike the passive nature of traditional supports, anchor cables are pre-tensioned, thus enabling the proactive stabilization of the surrounding rock. This difference underscores the active and swift control exerted by the anchor cables during tunnel deformation.

Fig. 11
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Comparative analysis of tunnel deformation patterns in similar tunnel projects without prestressed anchor cables: a vertical displacement; b horizontal convergence

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3.3 Deformation of the surrounding rock mass

The development of the maximum rock displacements at the seven monitoring points, i.e., DW1–DW7, is shown in Fig. 12a. The excavation of the upper bench resulted in a rapid increase in rock displacements at DW1 and DW2. Subsequently, a data gap occurred due to the rupture of the sensor conductor wire. This incident, recorded using a displacement meter, did not affect the data accumulated and recorded in the displacement meter. Upon the reconnection of the wire, accurate accumulated data recorded by the meter became accessible. Notably, linear interpolation during the rupture period may not fully capture the accurate deformation development. Nonetheless, the convergence observed at the two monitoring points after the closure of the initial support was evident. Moreover, the ongoing increase in rock displacements at DW3, DW4, …, and DW7 persisted even after the initial support closure, a point at which the deformation of the tunnel structure had already converged (Figs. 9 and 10). Specific increment of rock displacement, from the closure of initial support to secondary lining closure, can reach a maximum of 12.8 mm (at DW4), attributed to the creep behavior inherent in soft rocks. The creep tendency could potentially undermine the mechanical efficacy of the support system, which is discussed in the next section.

Fig. 12
figure 12

Development and distribution of the rock displacement: a development of the maximum rock displacements at seven monitoring points; b distribution of rock displacements with spline approximation

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Spline interpolation was employed to characterize the rock displacement distribution based on the displacement data gathered from DW1 to DW7 during the final stage, as shown in Fig. 12b. A significant disturbance zone was observed around both drifts, potentially attributed to persistent disturbances creep behavior across the entire excavation process. In addition, an extrapolation was conducted to establish a 0-mm displacement contour line. The dashed line separates the disturbance zone from the non-disturbance zone. The extent of the disturbance zone was approximately 12 m. Notably, the length of the prestressed anchor cables is 20 m, surpassing the extent of the disturbance zone. This suggests that the cables featured stable anchor ends, essential for the “shed-frame” system’s operation, thus enabling it to function collaboratively to withstand earth pressures.

4 Mechanical behaviors of the tunnel

4.1 Rock pressure on the tunnel

Figure 13a shows the development of rock pressure on the tunnel. Most monitoring points exhibited a consistent increase in the measured rock pressure during the excavation process. Notably, this upward trend persisted even after the initial support closure, attributed to the creep behavior of the rock mass, wherein the surrounding rock continued to deform and consequently imposed an additional load on the initial support. A further demonstration of this trend is evident from the increasing stress within the support system, as shown in Fig. 14. Therefore, timely closure of the secondary lining is important to ensure construction safety, particularly in projects involving soft rocks.

Fig. 13
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Monitoring results for surrounding rock pressure: a development of surrounding rock pressure; b final distribution of rock pressure

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Fig. 14
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Stress of steel frame in the initial support: a stress at the side close to the surrounding soft rock; b stress at the side away from the surrounding soft rock

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The distribution of the surrounding rock pressure upon completion of the excavation is depicted in Fig. 13b. The spatial distribution of the rock pressure around the tunnel was non-uniform, gradually diminishing from the tunnel vault to the invert and increasing along the sidewall. The highest rock pressure within the monitored section was recorded at the tunnel vault, reaching 245.4 kPa. Given a rock unit weight of 20 kN/m3, the height of the pressure arch can be approximately calculated as 12.3 m. In addition, an empirical formula from the standard allows the estimation of a typical height for soft rock, expressed as [10]:

$$h = 0.45 \times 2^{s - 1} \omega,$$
(4)
$$\omega = 1 + i(B - 5),$$
(5)

where h denotes the estimated height of the pressure arch, s denotes the rated rock types ranging from I to VI, B represents the span of the tunnel, and i is a regression parameter, equaling 0.1 when B exceeds 5 m. Given the characteristics of this project, an empirical height estimation yields 20.9 m using Eqs. (4)‒(5). However, the actual height was approximately 12.3 m, 41% lower than the estimated value, suggesting that, to a certain extent, prestressed anchor cables effectively bolster the surrounding rock and preserve its integrity, making them superior to traditional internal support schemes.

4.2 Stress of the steel frame

The stress within the steel frame of the initial support is shown in Fig. 14. Along the side adjacent to the surrounding rock mass, the compressive stress gradually increased with the excavation procedure and ultimately stabilized. However, during the early stages of the drift excavation, monitoring points P1-A and P2-A exhibited tensile stress, possibly attributed to the elevating effect of the prestressed anchor cables. Along the side adjacent to the tunnel surface, the compressive stress exhibited continuous growth across all monitored points before eventually converging, as depicted in Fig. 14b. The maximum compressive stress observed within the steel frame of the initial support was approximately 232 MPa (P1-B). This value remains below the standard axial compressive/tensile strength of the steel frame of 335 MPa [34, 45]. This finding also underscores an important role of the initial supports, which operate in synergy with the anchor cables to withstand earth pressures. This insight reinforces the design principle that advocates for an integrated consideration of the “shed-frame” system, thereby avoiding overly conservative design for the anchor cables.

Notably, removing the internal temporary supports does not result in any abrupt stress increase across the entire steel frame, thus suggesting that the removal process has a limited impact on the mechanical behavior of the initial support, attributed to the advanced tensioning of the prestressed anchor cables, which had already held the steel frame, thus mitigating the impact of support removal.

4.3 Axial forces of the anchor bolts

The development of the maximum axial forces in the seven monitored anchor bolts is shown in Fig. 15a. Positive values signify axial tension. The axial forces in MZ1 and MZ2 experienced the most rapid initial increase among the seven bolts and subsequently converged after the excavation of Part III. In contrast, MZ3 exhibited minimal changes during the excavation process. As discussed previously, the stable trend indicated that removing the temporary support had a limited impact on the mechanical behavior of the bolts. The ultimate distribution of the stabilized axial forces within the anchor bolts is shown in Fig. 15b. MZ1 and MZ2 exhibited the highest axial forces of 46.2 and 57.8 kN, respectively. Conversely, MZ3 exhibited a significantly lower axial force of 6.2 kN. These minimal values indicate a potentially suboptimal design or construction of the anchor bolts around the tunnel vault, suggesting further optimization required in the remaining sections.

Fig. 15
figure 15

Development and final distribution of axial forces in anchor bolts: a development of maximum axial forces in anchor bolts; b final distribution of axial forces in anchor bolts

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4.4 Prestress of the anchor cables

Multiple monitoring sections have been established for the anchor cables, revealing a common characteristic of significant prestress loss. Specifically, prestress losses were observed to range from approximately 14% to 38% in the section at DK288 + 220 and from 14 to 54% in the adjacent section at DK288 + 222. While detailed raw data for the section at DK288 + 220 can be found in [43], this paper utilizes the data from DK288 + 222 as an illustration for analyzing the working condition of the prestressed anchor cables.

The development of axial forces within the prestressed anchor cables at DK288 + 222 is presented in Fig. 16. Despite some missing data points attributable to the complexities of the construction environment, the available dataset was considered sufficient to evaluate the cables’ performance of post-stabilization. The analysis suggests that the majority of anchor cables maintained a relatively stable level of axial force (similar to the observations from DK288 + 220), except for AC-6, which initially exhibited significant fluctuations around approximately 250 kN. Overall, axial forces were observed to stabilize within a range between 230 and 430 kN. Notably, in cases where the prestressed axial force is insufficient for withstanding earth pressures, the anchor cables will undergo passive tensioning, resulting in an increase in axial force. Nevertheless, the observed axial forces were significantly lower than the design bearing capacity of 1041 kN, demonstrating substantial design redundancy. This redundancy might be attributed to the anticipated natural balance arch, based on Protodyakonov’s theory, which overlooks the impact of prestressed anchor cables. In fact, as revealed previously, the prestressed condition can effectively mitigate excavation-induced stress release in the surrounding rock mass. Consequently, future research should aim to refine the design methodology by more comprehensively considering the impact of anchor cables.

Fig. 16
figure 16

Development of prestress in the anchor cables

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Furthermore, although the design prestress was set at 500 kN, the final axial forces within various anchor cables (across different sections) ranged from 230 to 430 kN, indicating significant and varied prestress loss, and thereby suggesting design redundancy in prestressing as well. It is worth noting that such redundancy does not directly result in a reduction in prestress. This loss is primarily attributed to manual operations—particularly, the loss of prestress following the removal of the hydraulic jack used for cable tensioning. Consequently, it is essential to conduct further research aimed at mitigating the prestress loss during anchor cable installation, thereby enhancing anchoring efficacy and stability.

5 Conclusions

This paper introduces a novel support system for super-large-span tunnel excavations using prestressed anchor cables as an alternative to traditional internal supports. While this system offers a spacious working area, enhancing construction efficiency, its practical application in field settings is relatively unexplored. The key conclusions of our field-case analysis are as follows:

  1. 1.

    During excavation, the prestressed anchor cables integrated the initial support with the shed, forming an effective “shed-frame” system. This system operated synergistically to ensure that deformations and stress levels within the frame successively remained within safe and acceptable limits.

  2. 2.

    The prestressed anchor cables result in a distinctive “staircase-like” deformation pattern. This pattern implies active and rapid control over the tunnel deformation, in contrast to the continuous deformation observed with traditional internal supports. A 41% reduction in the pressure arch height compared to the empirical values further indicates the anchors’ ability to stabilize the surrounding rock.

  3. 3.

    It is notable that a limited number of internal supports are initially necessary, due to the time-intensive nature of constructing prestressed anchor cables. However, the subsequent removal of these supports has little impact on construction safety.

  4. 4.

    Creep behavior was evident in the surrounding soft rock. The persistent deformation of the surrounding rock imposed an additional load on the initial support. Notably, the presented support system enhances construction efficiency, facilitating timely secondary lining closure, thus making it especially advantageous for soft rock projects.

  5. 5.

    Areas for future research include (i) enhancing the technology and equipment to accelerate the installation of prestressed anchor cables, thereby eliminating the need for temporary support entirely; (ii) refining the design methodology of prestressed anchor cables to reduce redundancy; and (iii) developing methods to reduce the high loss of prestress in the anchor cables, observed to reach up to 54%.