A New Approach to Designing Advance Stress Release Boreholes to Mitigate Rockburst Hazards in Deep Boring-Machine-Constructed Tunnels

Abstract

The use of tunnel boring machines (TBMs) in deep hard rock tunnels disrupts the original stress equilibrium of the rock mass, often resulting in the aggregation and release of a large amount of elastic strain energy, and even leading to rockburst. Under extremely high rockburst proneness conditions, advance stress release boreholes (ASRBs) deployed behind the TBM cutter head can be used to reduce stress concentration levels. However, there is a lack of scientific design methods for the parameters of the ASRB program for TBM tunnels, leading to poor stress release and difficulty in mitigating high-intensity rockburst hazards. This study proposes a parameter design method for ASRBs in the potential rockburst seismic source area of deeply buried hard rock TBM tunnels, including test scheme establishment methods, parameter selection methods, and parameter space relationship and evaluation index establishment methods. A deep tunnel in southwest China was used as an engineering case study to explore the effect of stress release and energy dissipation under different ASRB layout schemes. The results show that the sensitivity of the five important design parameters of ASRBs to the stress release effect is, in descending order, “aperture”, “inclination”, “included angle”, “spacing”, and “length”. A parameter control law for ASRBs is proposed, which confirms their effectiveness in preventing, controlling, and reducing rockburst disasters in deep hard rock TBM tunnels.

1. Introduction

With the continuous development of underground engineering, the number of tunnels at a deep-buried depth and with large diameters is increasing [1,2,3]. The emergence and use of tunnel boring machines (TBMs) have greatly improved the efficiency of excavating and supporting deep tunnels. A TBM not only guarantees effective tunnel excavation progress with an average monthly footage of up to 1600 m [4], but also ensures the safety of construction personnel and equipment [5]. However, deeply buried hard rock TBM-constructed tunnels are still inevitably threatened by high-stress rockburst hazards [6,7], as shown in

Table 1. Information on rockburst hazards in selected deeply buried hard rock TBM tunnel projects.

Project Name	References	TBM-Constructed Tunnel Length/m	Maximum Overburden of Tunnel/m	Stratigraphic Lithology and Rock Strength (UCS/MPa)	Percentage of Length of Rockburst Section/%	Rockburst Mechanisms or Its Manifestation
Headrace Tunnel Project for the Jinping Cascade II Hydropower Station	(Hou et al. 2011, Yang et al. 2020) [13,14]	15,092	2525	T2b Marble: 70~100	SR: 16.85% MR: 6.29% IR: 3.43% ER: 4.46% Total: 31.03%	SR: folding and belling failure and extrusion and slabbing failure MR: structural plane-controlled failures or extrusion and slabbing failures
Qinling Tunnel in the Hanjiang–Weihe River Diversion Project	[15,16,17]	8521	2012	Quartzite, granite, and diorite: 107~317	Total: 41.65%	SR: flaky flaking type MR: between flaky flaking type and explosive ejection type IR: explosive ejection type
The Neelum Jhelum hydroelectric project	[18,19,20]	20,000	2000	Sandstone: 130~170	SR: 79.65% MR: 5.31% IR: 0.89% Total: 85.85%	SR: some light damage to the rock support and surrounding rock MR: spitting, spalling, or shallow slabbing to the rock support and surrounding rock IR: violent ejection of rock into the tunnel and severe damage to the installed support

Note: SR, MR, IR, and ER in the table stand for slight rockbursts, moderate rockbursts, intense rockbursts, and extremely intense rockbursts, respectively.

. Deep rockburst hazards may cause large volumetric collapses, rock cracking, ejection, or extreme bulking of hard rocks [8,9,10] and delay the construction process [11]. Therefore, effectively controlling the occurrence of rockbursts is one of the key problems to be urgently solved in current deeply buried tunnel projects [12].

As an effective means of rockburst prevention and control, advance stress release boreholes (ASRBs) have the advantages of simple construction, low cost, and low workload during construction [21], so they are widely used in deep tunnels under the condition of a high rockburst risk [22]. By strategically designing the layout parameters of ASRBs, it is possible to effectively release stress and energy from the surrounding rock mass, thereby altering the rockburst incubation process and preventing or controlling such incidents [23]. Advance stress release technology has been successfully applied to tunnels constructed by drilling and blasting. For example, Tian, Zhao [24], in the Bayu Tunnel of the Sichuan–Tibet Railway, effectively reduced the safety risk of rockbursts in the tunnel by taking measures such as advance geological prediction, rockburst microseism monitoring, construction of ASRBs in the face, injection of high-pressure water into the release boreholes to release stress, weak blasting at the bottom of the boreholes to loosen the rock mass, and “shotcrete + hanging net + anchor” support. The construction technology of deep-hole stress release blasting was adopted in the strong rockburst sections of the No. 3 and No. 4 headrace tunnels within the Jinping II Hydropower Station to reduce the possibility of a rockburst disaster during construction [25]. Konicek, Soucek [26] used a suitable stress relief blasting design scheme to pre-fracture the surrounding rock in advance in the Lazy Colliery in the Ostrava–Karvina Coal Field of the Upper Silesian Coal Basin, and the 300-m-long wall panels could be mined without further rockbursts. Wojtecki, Konicek [27] analyzed the tremor generated by long-hole stress release blasting during the mining of the 507 seam in a hard coal mine in the Polish part of the Upper Silesian Coal Basin, evaluated the stress release effect, and analyzed the dynamical mechanisms and impacts on the surrounding rock. Konicek, Saharan [28] introduced the research progress of stress release blast technology in many domestic and foreign coal mines; discussed its main advantages from the perspectives of geology, rock properties, mining conditions, and blasting parameters; and evaluated the effectiveness of the release effect. However, the TBM cutter head structure usually limits the layout of stress release boreholes, so the application of ARHs in TBM-constructed tunnels is rare. As a rare case, water hammer drill ASRBs were constructed at K40+613 in the TBM-constructed tunnel section of the Hanjiang–Weihe River Diversion Project [29,30]. Liu carried out microseismic monitoring and numerical simulation, and the results showed that ASRBs release energy within the rock mass to some extent [30].

There are very limited studies on the ASRB design method, most of which focus on the analysis of the correlation between the stress release effect and SRB parameters such as diameter, depth, spacing, and shape. From a test perspective, Wang, Jiang [31] conducted indoor experiments on samples with different borehole sizes, depths, and spacing. They obtained the correlation between borehole parameters and stress release effects. Xiao, Li [32] conducted indoor experiments and numerical simulations to explore the effects of the height and width of square boreholes on strain energy release. Zeng, Yang [33] conducted indoor uniaxial compression tests on prefabricated rock samples with different pore shapes, revealing the internal mechanism of drilling pressure release. From a numerical analysis point of view, Chen, Feng [34] discussed the effect of SRBs on the stress release and energy dissipation of rocks surrounding an auxiliary tunnel of the Jinping II Hydropower Station. The stress release and energy dissipation effects of an SRB under different schemes from the perspective of the plastic zone, damaged zone, and accumulated energy were analyzed. Jia, Jiang [35] discussed the stress release mechanism of large-diameter drilling from the perspective of indoor testing and particle flow code (PFC) simulation and analyzed the influence of borehole diameter, borehole depth, and borehole spacing parameters on the stress release effect. Zhang, Zhu [36] revealed the stress release mechanism of SRBs using a numerical simulation method and discussed the influence of three borehole parameters, namely, borehole diameter, borehole depth, and borehole spacing, on the stress release effect. However, in practical engineering applications, drilling parameters usually rely on empirical values, lacking reliable design and analysis methods [21]. Therefore, there is an urgent need for a set of ASRB parameter design methods applicable to TBM-constructed tunnels to solve the problems of limited advance stress release measures for TBM tunnels, insufficient design methods for the location of ASRBs, and the estimation of stress release and energy dissipation effects.

Given this, this paper proposes a design method for ASRB parameters in potential rockburst source areas of deeply buried hard rock TBM tunnels and analyzes the influence of five borehole parameters (inclination, length, included angle, aperture, and spacing) on the stress release effect using a section of a deeply buried tunnel project in southwest China. This method establishes a parameter design methodology for ASRBs and a technique for their effectiveness evaluation, including test scheme establishment methods, a parameter selection method, the parameter space relationship, and an evaluation index establishment approach. The analysis process ensures that the layout of the ASRBs is optimized to maximize the stress release effect with no change in the construction workload of the project. The resulting stress release borehole parameters can be used in the stress release borehole design scheme for the pre-digging period of deeply buried TBM-constructed tunnels and provide a data basis and suggestions for the optimization of the stress release borehole parameters after obtaining more abundant field data. The proposed method and the obtained conclusions are expected to be applied for the prevention, control, and mitigation of rockburst hazards in deep hard rock TBM tunnels.

2. Stress Release and Energy Dissipation Mechanisms of TBM Tunnel ASRBs

As the TBM tunnel face advances, based on elastic–plastic mechanics theory and the distance from the surrounding rock, the excavation damage zone (EDZ) and the original rock stress zone is formed in the surrounding rock [37], where the maximum principal stress concentration area is located at the junction of the EDZ and the original rock stress zone, as shown in Figure 1a. Near the TBM cutter head, the maximum principal stress concentration is close to the side wall, and the hard rock mass in this area has accumulated a large amount of elastic strain energy under the action of high ground stress [38], thus forming a potential rockburst source area, threatening the safety of engineering equipment and construction personnel. To ensure the smooth progress of TBM tunneling and to prevent geologic hazards such as jamming or rockbursts, it is necessary to release the energy in the rock around the TBM cutter in advance. For this reason, in the limited space behind the cutter head, the high stress and elastic strain energy in the maximum principal stress concentration area can be released in advance by reasonably applying ASRBs and using their stress release and energy dissipation effects, as shown in Figure 1b, to effectively reduce the possibility of a rockburst in the surrounding rock during TBM tunneling.

In tunnels constructed by the drilling and blasting method, SRBs are often constructed in the side wall, top arch, and face of the tunnel, depending on the different target areas for stress release, as shown in

Table 2. Common layout of stress release boreholes (SRBs) in deep hard rock tunnels constructed by the drilling and blasting method.

Layout Location	Schematic Diagram of the Drilling Design Scheme	Applied Tunnel Engineering	References	The Specific Layout of the SRBs
Tunnel side wall		Zaoquan Coal Mine Project	[39]	SRBs are staggered in the side wall of the tunnel, such that the distance between transverse SRBs is 1.5 m, the distance between rows is 0.5 m, and the borehole diameter is 100 mm.
Tunnel arch position		Water Diversion Project from Han River to Wei River	[30]	The 13 SRBs are symmetrically and evenly arranged at the top arch of the tunnel, with an aperture of 89 mm, a borehole depth of 5.0 m, and a borehole elevation of 15°
Tunnel face position		Headrace Tunnel Project for Jinping Cascade II Hydropower Station, Bayu Tunnel Project	[41,42]	The SRBs are uniformly arranged along the excavation contour or on the circumference at a certain distance from the excavation contour and arranged in multiple rows according to different stress concentrations.

. Research in the field of coal mining has found that reasonable placing of SRBs in high-stress roadways can improve the stress environment of the surrounding rocks in the following two ways: (1) SRBs release energy accumulated in the surrounding rock masses, transfer the stress concentration area to deep areas, and reduce the stress concentration degree [39]; and (2) the drilling process can lead to structural pre-splitting failure of the roadway-surrounding rock, thus reducing its brittleness and ability to store elastic strain energy [40].

To obtain a simple simulation process for the unloading mechanism of the stress release borehole in general, FLAC^3D 6.0 finite difference software [43] was used, and the simulation results under different SRB deployment scenarios are shown in Figure 2. In this case, granite was specified for analysis, and its mechanical parameters are listed in

Table 3. Model calculation parameters.

Parameters	Value
Young’s modulus/GPa	20.00
Poisson’s ratio	0.25
Dilation angle/°	10.00
Initial cohesion /MPa	12.60
Plastic strain limit of cohesion	0.004
Residual cohesion /MPa	8.52
Initial internal friction angle/°	10.00
Plastic strain limit of internal friction	0.005
Residual internal friction angle/°	35.00

. The maximum principal stress distribution after the application of SRBs was simulated under the initial geostress conditions of ${\sigma }_1$ = 39.38 MPa, ${\sigma }_2$ = 31.14 MPa, and ${\sigma }_3$ = 27.63 MPa. The simulation results show that certain stress concentration areas and stress release areas can be formed around a single SRB (Figure 2a). When two SRBs work together, the stress release area overlaps to form a larger release area (Figure 2b). Moreover, after the construction of multiple SRBs, the stress release area will overlap and converge into an unloading zone (Figure 2c). Under different borehole parameter conditions, SRBs modify the original concentrated stress field to different degrees through the damage zones. By optimizing the borehole parameters, the regional stress release effect of SRBs will be improved, the original stress concentration degree will be reduced, and the high-stress-concentration area will be transferred to the deep high-strength and high-energy storage rock mass.

However, TBM-constructed tunnels are unique because of their circular cross-section, the difficulty of withdrawing the TBM equipment, and the simultaneous excavation, slag removal, and support processes. Due to the limited space behind the cutter head, the layout of the stress release boreholes is limited to the two sides of the tunnel. As shown in Figure 3, the extension of the drilling equipment accompanying the TBM instrument and the stress concentration areas in the surrounding rock limit the layout of the SRBs. In this case, the release borehole layout is usually chosen based on the extent of the release area and the desired release effect. For example, if the location of a potential rockburst source area is precisely determined and a high-stress-release effect is needed, the parallel deployment shown in Figure 3a will create a denser SRB, which will achieve a higher stress release effect. When the location of the source area is uncertain, or when the proximity to the tunnel surface does not require a high level of stress release effectiveness, the use of the dispersive placement shown in Figure 3b will be more effective for enhanced stress release. Therefore, due to the special characteristics of TBM tunnels, the stress release scheme will be largely different from that of tunnels constructed by drilling and blasting. On the one hand, construction-space-limiting SRBs can only be arranged in advance, and so are also known as advance stress release boreholes (ASRBs). On the other hand, due to the special arrangement of the SRBs, the existing drill-and-blast stress release technology cannot be fully applied to TBM tunnels.

Table 4. The comparison of different tunnel stress release techniques.

Stress Release Techniques	Application Scenario	Control Parameters for Stress Release Effect	Advantages	Disadvantages
Stress release blast technique	Tunnels constructed by the drilling and blasting method	Length, spacing, borehole location, explosive quantity, etc.	Good stress release effect, short construction period, mature process and easy to apply on the project site	Release borehole parameters rely on empirical values, the blasting effect is not easy to control, and preliminary blasting tests need to be carried out in the field beforehand.
SRBs	Tunnels constructed by the drilling and blasting method	Length, spacing, borehole location, etc.	Short construction period, controlled release effect, low construction costs, and mature technology	Limited stress release effects and difficult to carry out in TBM-constructed tunnels
High-pressure water injection drilling	Drilling and blasting method and TBM-constructed tunnel	Length, spacing, borehole location, water injection pressure, water injection time, etc.	Reduces the strength of the surface layer of the surrounding rock, facilitates the emergence and expansion of fractures, and reduces the integrity and energy storage capacity of the rock mass	Water injection has a limited impact and limited stress release, and often needs to be combined with other stress release measures to be effective.
ASRBs	TBM-constructed tunnel	Length, spacing, inclination, included angle, aperture, etc.	Stress release technology for deep-buried hard rock TBM-constructed tunnels with simple procedures, low cost, and controllable release effect	Limited stress release effect and difficulty in applying tunnel palm faces

shows the comparative information of several common stress release techniques, which shows that ASRBs have more prominent advantages over other stress release techniques in deep-buried hard rock TBM-constructed tunnels.

Therefore, the research on ASRB technology needs to be developed urgently. Considering the complexity of the field construction environment, the following two special stress release strategies for TBM tunnels are ignored to obtain the correlation law between the parameters of ASRBs and the stress release effect under the prevailing conditions. (1) TBMs cannot drill boreholes in the working face of tunnels because there are still some technical difficulties in using TBM equipment that can drill boreholes in the working face. (2) A pilot tunnel is first constructed, and then TBM tunneling is carried out, similar to the stress release measures at the face of the Jinping II headrace tunnel [44,45]. The research conditions in this paper consider only the general situation of ASRB arrangement on both sides behind the cutter head in the TBM tunnel. The design methodology for the corresponding ASRB parameters during the construction of TBM tunnels is determined and summarized.

3. Parameter Design Method of TBM Tunnel ASRBs

Based on the analysis of the above SRB stress release mechanism, this study proposes a design method for the ASRB parameters in TBM tunnel construction under high-rockburst-risk conditions, which includes test scheme establishment method, a parameter selection method, the parameter space relationship, and an evaluation index establishment method, as shown in Figure 4. The general process is to first identify the potential rockburst area in the TBM tunnel, i.e., to determine the study area for the ASRB parameter design. Second, the rockburst source area in the high-rockburst-risk section is determined, i.e., to determine the stress release area within the study area. Third, the borehole parameter design method is determined, and a preliminary ASRB design scheme is developed. Fourth, the test results are analyzed to derive the correlation between each borehole parameter and the release effect. Finally, the optimal layout of the ASRB that best meets engineering best practices is determined.

3.1. Evaluation of Rockburst Grade in Deeply Buried Hard Rock TBM Tunnels

In rock engineering with rockburst risks, the evaluation of rockburst grade is crucial for designing support structures and risk prevention and control measures [46]. In the pre-construction phase of the project, assessing the rockburst grade can provide a reference for the resolution of the excavation method and hazard prevention measures [47]. Therefore, before conducting the ASRB design scheme for TBM tunnels, rockburst grading along the tunnel should be determined based on the engineering geological conditions, geostress field conditions, and relevant construction design parameters of the project area, such as tunnel burial depth, excavation diameter, etc. With increasing research on the rockburst mechanism, many rockburst classification methods have been proposed [48]. According to the number of factors used in the theoretical and empirical criteria, the assessment methods of rockburst grade can be divided into single-factor and composite-factor criteria. Among these, single-factor theoretical criteria include the strength criterion (Tao Zhenyu criterion [49], the Turchaninov criterion [50], the Russenes criterion [51], etc.) and the energy criterion (strain energy storage index [52], the stiffness criterion (brittleness coefficient [53], etc.). Composite-factor criteria include the empirical rockburst vulnerability index (RVI) [54] and excavation vulnerability potential (EVP) [55].

Table 5. The common theoretical and empirical criteria for rockburst grade assessment [48].

Type	Criterion	References	Assessment Indexes	Rockburst Grade Assessment Results
				None	Slight	Moderate	Intense
Single-factor criteria	Tao Zhenyu criterion	[49]	${\sigma }_c/{\sigma }_1$	[14.5,+∞)	[5.5,14.5)	[2.5,5.5)	[0,2.5)
	The Turchaninov criterion	[50]	$({\sigma }_{\theta }+{\sigma }_l)/{\sigma }_c$	[0,0.3)	[0.3,0.5)	[0.5,0.8)	[0.8,+∞)
	The Russenes criterion	[51]	${\sigma }_{\theta }/{\sigma }_c$	[0,0.2)	[0.2,0.3)	[0.3,0.55)	[0.55,+∞)
	Strain energy storage index	[52]	${\varphi }_{sp}/{\varphi }_{st}$	[0,2.0)	-	[2.0,5.0]	[5.0,+∞)
	Brittleness coefficient	[53]	$\alpha {\displaystyle \frac{{\sigma }_c{\epsilon }_f}{{\sigma }_t{\epsilon }_b}}$	[0,3.0]	(3.0,5.0)	[5.0,+∞)	-
Composite-factor criteria	Rockburst vulnerability index	[54]	$F_s{F}_r{F}_m{F}_g$	-	-	-	-
	Excavation vulnerability potential	[55]	$E_1{E}_3/E_2{E}_4$	[0,50.0)	[50.0,85.0)	[85.0,105)	[105,+∞)

Note: ${\sigma }_c$ is the uniaxial compressive strength of the rock, ${\sigma }_1$ is the maximum principal stress, ${\sigma }_{\theta }$ is the maximum tangential stress, ${\sigma }_l$ is the maximum axial stress, ${\varphi }_{sp}$ is the elastic strain energy (density), ${\varphi }_{st}$ is the dissipated energy (density), ${\sigma }_t$ is the uniaxial tensile strength of the rock, $\alpha$ is the adjustment parameter, ${\epsilon }_f$ and ${\epsilon }_b$ are the strain in the pre-peak and post-peak regions under uniaxial compression conditions, $F_s$ is the stress control factor, $F_r$ is the rock petrophysical factor, $F_m$ is the rockmass system stiffness, $F_g$ is the geologic structure factor, $E_1$ is the stress condition parameter, $E_2$ is the ground support parameter, $E_3$ is the excavation span parameter, and $E_4$ is the geological structure parameter.

lists the theoretical and empirical criteria that are commonly used to assess the rockburst grade.

Based on the assessment methodology listed above, an assessment of the rock burst grade along the TBM tunnels can be carried out to determine the rockburst grade of the unexcavated tunnel sections. It is essential to carefully evaluate the implementation of ASRBs specifically for tunnel sections at high risk of intense or extremely intense rockbursts. The rationale behind this consideration stems from the potentially severe consequences associated with rockburst incidents in these tunnel sections. The occurrence of intense or extremely intense rockbursts in these sections has the potential to endanger the safety of TBM equipment and construction operations, and even destroy the TBM equipment, leading to significant casualties. This unfortunate scenario previously unfolded during the construction of the TBM-constructed drainage tunnel at the Jinping II Hydroelectric Power Station, where the TBM became buried and its main beam fractured, resulting in the loss of seven lives [56,57].

3.2. Identification of Potential Rockburst Source Areas in Deeply Buried Hard Rock TBM Tunnels

When a TBM is tunneling in an area with an intense or extremely intense rockburst risk, the surrounding rock will accumulate a large amount of elastic strain energy [58]. If the accumulated elastic strain energy exceeds the minimum energy storage limit, the excess strain energy will be quickly released, resulting in serious dynamical rupture and even rapid ejection of the rock mass around the tunnel, which is a rockburst [23,59]. Therefore, when TBM-tunneling into a tunnel section with an intense or extremely intense rockburst risk, it is essential to accurately identify the high-ground-stress and high-elastic-strain-energy-concentration areas and to arrange ASRBs accordingly.

Several suggested methods can be used to identify potential rockburst source areas in TBM tunnels, as shown in Figure 5. The first method is the microseismic (Figure 5a) and acoustic emission (Figure 5b) monitoring method, which collects information on the fracturing damage of the surrounding rock and uses areas of fracture concentration to identify potential rockburst seismic source areas. The second method is the disturbed stress monitoring method (Figure 5c), which infers the location of the potential rockburst seismic source areas by monitoring the change in stress increments at different depths of the surrounding rock. The third method is numerical simulation, which involves summarizing the field engineering data, carrying out numerical calculations, and using a variety of indicators such as the local energy release rate (Figure 5d), maximum principal stress (Figure 5e), elastic strain energy, etc., to determine the location of the potential rockburst seismic source areas. The identification of potential rockburst seismic source areas can be determined through a combination of the three methods mentioned above.

3.3. Test Scheme Determination for ASRBs and Method for Evaluating Their Stress Release Effect

Under the premise of a preliminary determination of the potential rockburst seismic source areas, the test analysis methods were selected reasonably, and the matching test scheme and evaluation indexes of stress release and energy dissipation effect were established to evaluate the ASRB parameters of TBM-constructed tunnels in a refined way.

3.3.1. Selection of Test Analysis Method

In terms of the test analysis methods, commonly used parameter law analysis methods include the comprehensive test, the control variable method test, and the orthogonal test, among others. The differences between the test analysis methods are shown in

Table 6. Comparison of test analysis methods for different ASRB parameters.

Test Analysis Methods	Design Ideas	Advantages of the Design Method	Disadvantages of the Design Method	Design Content	Number of Tests
Comprehensive test	Simulate and analyze all combinations	The correlation between borehole parameters and release effect can be analyzed	The number of research and simulation cases will be too large	All possible combinations of borehole parameters	${\displaystyle \prod _{i=0}^m}{n}_i$
Control variable method test	Analyze each borehole parameter in turn among various borehole parameters	The number of tests can be greatly reduced, and some important factors can be analyzed separately	The research scheme is not comprehensive enough, and the interference between different factors may be ignored	A parameter combination scheme when one factor changes and the others remain unchanged	${\displaystyle \sum _{i=0}^m}{n}_i$
Orthogonal test	Use the orthogonal table to arrange the test content	The number of tests is greatly reduced, and the correlation between various factors can be analyzed	The research program is not comprehensive enough	A combination scheme designed according to the orthogonal table	$[{\displaystyle \sum _{i=0}^m}{(n}_i-1)]+1$

Note: $m$ in the table represents the number of test factors, and $n_i$ represents the number of factor levels of the ith factor.

.

3.3.2. Selection of Design Parameters

After determining the test analysis methods, based on the stress release mechanism of ASRBs mentioned in Section 2, the layout parameters of ASRBs and the corresponding test scheme can be determined. Regarding the design parameters of ASRBs, two types of ASRB parameters need to be considered: the geometric parameters of the boreholes themselves and the distance parameters between the boreholes. The former is often determined by the relevant drilling equipment and engineering construction requirements of the ASRBs on the site, including borehole diameter and borehole depth parameters. The latter can be rationally designed based on the extent of the stress release area and the expected stress release effect, as shown in Figure 3. The ASRBs can be parameterized by selecting the parallel or divergent arrangement method to determine the distance between the ASRBs to be designed. Based on the determination of the parameters and potential rockburst seismic source areas, the initial ASRB design scheme can be determined. The parameters of location $d$ (distance from the palm face), inclination $\theta$, length $l$, row spacing $r$, interval $h$ (in case of parallel placement), and angle $\alpha$ (in case of divergent placement) of the initial ASRBs can be calculated using the following formula.

$$d=d_c+d_p+{\displaystyle \frac{l_p}{2}}+{\epsilon }_1$$

(1)

$$\theta =\arctan \left({\displaystyle \frac{r_p}{d-d_p}}\right)$$

(2)

$$l=r_p\mathrm{c}\mathrm{o}\mathrm{s}\theta +{\epsilon }_2$$

(3)

$$r={\displaystyle \frac{l_p}{m-1}}$$

(4)

$$h={\displaystyle \frac{h_p}{n-1}}$$

(5)

$$\alpha ={\displaystyle \frac{{\alpha }_p}{n-1}}$$

(6)

As shown in Figure 6, in equations 1 to 6, $d_c$ is the length of the TBM cutter head, $d_p$ is the distance of the potential rockburst seismic source area from the palm face, $l_p$ is the length of the potential rockburst source area, ${\epsilon }_1$ is other distances that cause the ASRBs to be pushed back from their deployment locations, $r_p$ is the distance of the potential rockburst source area from the tunnel sidewalls, ${\epsilon }_2$ is the redundancy length, which should be greater than half the width of the potential rockburst area, $m$ is the row number of ASRBs, $h_p$ is the height of the potential rockburst area, which should be less than the diameter of the tunnel, $n$ is the row number of ASRBs in the vertical section, and ${\alpha }_p$ is the distributional angle of the potential rockburst area.

3.3.3. Selection of Test Scheme

The content of the test scheme is related to the test analytical method, as shown in the design content column of Table 6. In the process of establishing the test scheme, it is necessary to consider the spatial geometric relationship between the parameters to prevent crossover or overlap between ASRBs. The spatial relationship between the borehole parameters and the target stress release area also needs to be considered to ensure that the release area of the ASRBs largely overlaps with the target area.

3.3.4. Establishment of Test Scheme Indicators

In the process of simulating the established ASRB arrangement scenarios, it is important to statistically measure the changes to compare the differences in stress release effects under the different test scenarios. This is especially true considering that in deep-buried TBM-constructed tunnels, the mechanical behavior of the rock mass is closely related to various factors, such as ground stress conditions, lithology, tectonics, the excavation method, and the support system. The above factors will ultimately determine the stress state and energy accumulation in the rock mass and create the breeding conditions for rockburst. At the same time, the numerical simulation process should make it easy to quantify the test scheme indicators, so the evaluation indexes used are usually developed in terms of stress and energy. These two test indicators serve two purposes. Firstly, they are used to investigate the effect of stress and energy release under different types of ASRBs. Secondly, they are utilized for the comparative analysis of conclusions. If the two conclusions match, it provides further proof of the reliability of the results.

(1)

Stress aspect

From the viewpoint of stress, the change in the maximum principal stress can be taken as the embodiment of the ASRB stress release effect to compare the stress release effect under different ASRB arrangements. Therefore, the average stress release rate calculated by Equations (7) and (8) can be used as an evaluation index of the stress release effect of ASRBs under different schemes.

$${\varphi }^i={\displaystyle \frac{{\sigma }_{before}^i-{\sigma }_{after}^i}{{\sigma }_{before}^i}}\times 100\%$$

(7)

$$\mathsf{\Phi }={\displaystyle \frac{\sum _{i=1}^n{\varphi }^i}{n}}$$

(8)

Within the equations above, ${\varphi }^i$ is the maximum principal stress release rate at the ith measuring point, $\mathsf{\Phi }$ is the average stress release rate at all measuring points, ${\sigma }_{before}^i$ is the maximum principal stress value of the ith monitoring point before drilling (unit: Pa), ${\sigma }_{after}^i$ is the maximum principal stress value of the ith monitoring point after drilling (unit: Pa), and $n$ is the number of monitoring points.

(2)

Energy aspect

From the viewpoint of energy, the unit elastic strain energy (Equation (9)) is used as the index of energy calculation in this study, and the change in elastic strain energy in the monitoring area before and after drilling the ASRBs is used as the embodiment of the ASRB energy dissipation effect. Note that because the calculation of energy is related to the total volume of the elements involved in the calculation, the reason for the large change in the elastic strain energy under a certain arrangement of ASRBs may be the large calculation area of the scheme. To circumvent inconsistencies in the calculation area size across different schemes and prevent errors, Equation (10) normalizes both energy change and volume by dividing them. The average volume release energy can be obtained to compare the release effect of energy under different arrangement schemes.

$${\pi }^i={\displaystyle \frac{{\sigma }_1^2+{\sigma }_2^2+{\sigma }_3^2-2\nu ({\sigma }_1{\sigma }_2+{\sigma }_2{\sigma }_3+{\sigma }_1{\sigma }_3)}{2E}}$$

(9)

$$\mathsf{\Pi }={\displaystyle \frac{\sum _{i=1}^n[\left({\pi }_{before}^i-{\pi }_{after}^i\right)\times V_i]}{V}}$$

(10)

Above, ${\pi }^i$ is the elastic strain energy under the average volume of the ith unit (unit: J/m³), $\mathsf{\Pi }$ is the average volume release energy in the energy calculation area (unit: J/m³), and ${\sigma }_1$, ${\sigma }_2$, and ${\sigma }_3$ are the maximum principal stress (unit: Pa), intermediate principal stress (unit: Pa) and minimum principal stress (unit: Pa) at the centroid of the element, respectively. $\nu$ and $E$ are Poisson’s ratio and the elastic modulus (unit: Pa) of the element, ${\pi }_{before}^i$ is the elastic strain energy density of the ith unit before drilling (unit: J/m³), ${\pi }_{after}^i$ is the elastic strain energy density of the ith unit after drilling (unit: J/m³), $V_i$ is the volume of the ith unit (unit: m³), n is the number of units involved in the calculation, and $V$ is the sum of the unit volumes involved in the calculation (unit: m³).

3.4. Analysis and Design Optimization of ASRB Parameters

Based on the engineering geological conditions, the geological stress field conditions, and the relevant construction design parameters (e.g., tunnel burial depth, excavation diameter, etc.) of the project area, the influence of the ASRB design parameters on the stress release and energy dissipation effects, as well as the correlation between the parameters of ASRBs, can be obtained based on the previous studies.

The analysis needs to be conducted from two perspectives: sensitivity analysis and correlation analysis. The sensitivity analysis aims to evaluate the impact of each parameter related to ASRBs on the stress release and energy dissipation effects. The effect of a given parameter can be demonstrated by calculating the magnitude of range as shown in Equation (11), where $R$ is the range, $N_{max}$ is the maximum value of the test scheme indicator when the parameter is varied, and $N_{min}$ is the minimum value of the test scheme indicator. By comparing the range of stress release effects at different parameter values, the priority of ASRB parameter adjustments can be determined.

$$R=N_{max}-N_{min}$$

(11)

The correlation analysis aims to identify and examine the relationship between each ASRB parameter and the stress release and energy dissipation effects. This analysis aids in defining a strategy to optimize and adjust ASRB parameters. Ultimately, this approach facilitates the improvement of the existing design scheme or the suggestion of a more practical layout for ASRBs.

3.5. Selection of the Optimal ASRB Layout Plan in Line with Engineering Best Practices

According to the optimization and adjustment strategy, the optimal ASRB layout scheme in line with engineering best practices can be determined. Based on existing field investigation data and test data, the stress release effect of the optimal ASRB layout can be estimated using the same numerical simulation method as that used in the law analysis above. Since the ASRB parameters in the optimized scheme may not be consistent with any of the test schemes, a preliminary test of whether the optimized scheme is superior to the tested test schemes can be made by comparing the stress release effect of the optimized scheme with the results of the test schemes. At the same time, the parameter optimization strategies obtained through correlation and sensitivity analysis can be validated, and the optimization effect of the optimization ASRB layout can be initially estimated.

4. Engineering Application of the ASRB Parameter Design Method

Based on the above design method for ASRB parameters for deeply buried hard rock TBM tunnels, the following is an example of a deeply buried headrace tunnel project in southwest China to demonstrate the engineering application of the method.

4.1. Engineering Background

The ASRB design solutions vary depending on ground stress, tunnel size, lithology, and excavation method. To this end, the following is an example of a deep diversion tunnel project in southwestern China to illustrate the application of the above methodology. The engineering geological profile and tunnel cross-section design are shown in Figure 7 and Figure 8, respectively. The tunnel engineering area was the one with the strongest tectonic activity and the fastest geomorphic evolution on the Earth today. The tunnel was 38 km long, and the maximum buried depth reached 1673.5 m. Moderate-to-intense rock bursts may occur along the route. Therefore, the project used the open TBM method as the primary construction method and the drill and blast method as the auxiliary method. The project also fully considered the impact of rockbursts on the TBM equipment, which was equipped with high-efficiency advance drilling equipment to facilitate deep surrounding rock stress release when necessary.

This study was based on the rockburst assessment results along the tunnel and took the section near the high-stress-risk area of the tunnel (CK1247-CK1248, blue box position in Figure 7) as the study area. According to the results of in situ hydraulic fracturing and in situ stress field inversion, the initial geostress state of the area was ${\sigma }_H$ = 39.38 MPa, ${\sigma }_h$ = 31.14 MPa, and ${\sigma }_z$ = 27.63 MPa. The minor deviation between the intermediate principal stress direction and the tunnel axis was ignored during the study. The maximum principal stress direction was set as the vertical direction, the intermediate principal stress direction was consistent with the tunnel axis direction, and the minimum principal stress was perpendicular to the tunnel axis. The lithology of the study area was mainly Himalayan granite. To better simulate the true mechanical behavior of rock masses, a rock deterioration model (RDM) was selected for this simulation study [64]. This model is widely used in various deep hard rock engineering projects, such as for the marble in the pilot tunnels of the Jinping II Hydropower Station [63], and can accurately depict the high-stress fracture damage process of hard rock with weakened cohesion and strengthened friction, as shown in Figure 9. Based on the indoor test results, the elastic modulus, Poisson’s ratio, initial friction angle, and initial cohesion parameters of the rock mass were obtained. On this basis, the remaining parameters were continuously adjusted to fit the depth results of the surrounding rock damage zone, and the simulation parameters were finally determined, as shown in Table 3. The bottom, right, and rear parts of the model (with the negative direction of the X-axis as the dominant visual direction) were constrained, and the initial element stress values were set to ${\sigma }_x=31.14 \mathrm{M}\mathrm{P}\mathrm{a}$, ${\sigma }_y=27.62 \mathrm{M}\mathrm{P}\mathrm{a}$, and ${\sigma }_z=39.38 \mathrm{M}\mathrm{P}\mathrm{a}$. The simulation results of tunnel excavation based on the above parameters are shown in Figure 10a. The figure shows that the depth of the tunnel surrounding the rock EDZ was 2~3 m, which is consistent with the measured results (Figure 10b,c).

4.2. Scheme Design and Effect Evaluation of ASRBs

Based on the analysis of the stress release mechanism of ASRBs and the distribution of the maximum principal stress in the surrounding rock of the tunnel, the ASRB layout plan was designed. According to the simulation results presented in Figure 10 and considering the challenges involved in cutter head construction during TBM tunneling, as well as the convenience of implementing side wall stress release boreholes, the ASRB layout scheme depicted in Figure 3b was selected as the most suitable option. Thus, the drilling of ASRBs was scheduled to ensure their early integration in the stress adjustment process [21]. As a result, ASRBs were used for stress adjustment in the surrounding rock to reduce the stress concentration degree within the range of one tunnel diameter fore and one aft of the current tunneling head.

4.2.1. Determination of Test Analysis Method

Considering that the number of ASRB parameters considered in the study was more than that of the traditional drilling and blasting method for vertical rock wall drilling, the orthogonal test analysis method was adopted, which greatly reduces the number of tests.

4.2.2. Determination of Design Parameters

Combined with the design content of the ASRB scheme in Section 3.3, for the ASRB parameter design, the engineering focus was on the geometric parameters of the layout plan, including the length and aperture parameters. Previous studies have found that the distance parameter between boreholes also has a significant control effect on the energy released. Therefore, the angle, inclination, and spacing parameters need to be determined during the construction process. Hence, the factors of this ASRB parametric orthogonal test program were determined to be inclination, length, included angle, aperture, and spacing. The physical meaning of each factor is as follows:

• Inclination: the included angle between the ASRB axis and the tunnel axis (unit: °).
• Spacing: the axial spacing of the tunnel between the ASRBs of adjacent rows (unit: m).
• Length: the distance from the borehole bottom to the tunnel side wall in the ASRB (unit: m).
• Included angle: the sharp angle between the two adjacent ASRBs on one side of the tunnel cross-section and the line connecting the tunnel center (unit: °).
• Aperture: the diameter of the circle on the cross-section of the ASRB (unit: m)

The physical meaning of the design parameters is shown in Figure 11.

4.2.3. Determination of Test Scheme

Considering the above five factors of inclination, length, included angle, aperture, and spacing, with the construction form of an L¹⁶ (4⁵) standard orthogonal table, the level of each factor was determined as four. The geometric relationship between the parameters was taken into account when taking the specific value, and the unloading area of ASRBs overlapped, with the target area of the stress release being as great as possible. At the same time, the change range of each level was unified to reduce the extreme impact caused by an inconsistent change range. Finally, the factor level was set according to the results shown in

Table 7. The level of each factor in the orthogonal test.

Factors	Factor Level
	1	2	3	4
Inclination (°)	13.00	14.30	15.60	16.90
Length (m)	30.00	33.00	36.00	39.00
Included angle (°)	10.00	11.00	12.00	13.00
Aperture (m)	0.20	0.22	0.24	0.26
Spacing (m)	2.00	2.20	2.40	2.60

. Accordingly, the established orthogonal test scheme is shown in

Table 8. The orthogonal test design scheme.

Experiment Number	Inclination (°)	Length (m)	Included Angle (°)	Aperture (m)	Spacing (m)
1	13.00	30.00	10.00	0.20	2.00
2	13.00	33.00	11.00	0.22	2.20
3	13.00	36.00	12.00	0.24	2.40
4	13.00	39.00	13.00	0.26	2.60
5	14.30	30.00	11.00	0.24	2.60
6	14.30	33.00	10.00	0.26	2.40
7	14.30	36.00	13.00	0.20	2.20
8	14.30	39.00	12.00	0.22	2.00
9	15.60	30.00	12.00	0.26	2.20
10	15.60	33.00	13.00	0.24	2.00
11	15.60	36.00	10.00	0.22	2.60
12	15.60	39.00	11.00	0.20	2.40
13	16.90	30.00	13.00	0.22	2.40
14	16.90	33.00	12.00	0.20	2.60
15	16.90	36.00	11.00	0.26	2.00
16	16.90	39.00	10.00	0.24	2.20

. The orthogonal test only needed 16 tests, while the comprehensive test needed 4⁵ tests, i.e., 1024 tests. The orthogonal test method greatly reduced the number of tests.

4.2.4. Determination of Test Scheme Indicators

According to the description in Section 3.3.4, the average stress release rate and the average volume release energy were used in this study as the evaluation indexes of the stress release and energy dissipation effects of ASRBs under different scenarios. In the monitoring location, for the stress and energy distribution pattern after the deployment of ASRBs, the monitoring area as shown in Figure 12 and Figure 13 was used in this study for the calculation of test indexes, respectively.

(1)

Stress aspect

From the viewpoint of stress, the stress release effect was examined within the range of one tunnel diameter fore and one aft of the current tunneling head this study. Therefore, the face of the current tunneling head and the cross-section at both 0.5 diameters and one diameter fore and one aft of the current tunneling head were selected as the monitoring sections (Figure 12a). In addition, the stress release area was mainly concentrated between adjacent boreholes on one side of the tunnel cross-section, so the midpoint position on the arc connecting two adjacent boreholes on one side of each monitoring section was selected as the monitoring point, as shown in Figure 12b.

(2)

Energy aspect

From the perspective of energy, the energy calculation area was arranged as shown in Figure 13 in combination with the distribution of the stress release area mentioned above. Along the TBM tunneling direction, the area encompassing one tunnel diameter fore and one aft of the current tunneling head was divided into four energy monitoring areas, each one half the tunnel diameter in length. Each monitoring area extended along the axis of the ASRB. At the cross-section of the tunnel, to reduce the interference of stress and energy concentrations on the results in the monitoring area, it was only extended to the location of one diameter of the borehole wall, and the inner diameter and outer diameter of the monitoring area were constrained by the axial position of the inner and outer ASRBs to plan the regional distribution of energy calculation.

4.3. Analysis and Design Optimization of ASRB Parameters

4.3.1. Orthogonal Test Results

According to the design process of the orthogonal test scheme, the TBM excavation simulation model of ASRBs was built sequentially, as shown in Figure 14. The model dimensions and the grid cell sizes of the corresponding parts were the same for each scheme, but there were differences in the layout schemes of the ASRBs. During the simulation of TBM tunnel excavation, the drilling process of ASRBs was carried out sequentially. The excavation simulation was conducted for 16 groups of models to derive the maximum principal stress data of the corresponding monitoring points and the elastic strain energy of the corresponding calculation area. The results of the average stress release rate and average volume release energy for each ASRB deployment scenario are shown in

Table 9. Summary of the orthogonal test results.

Experiment Number	Average Stress Release Rate (%)					Average Volume Release Energy (KJ/m3)
	I	II	III	IV	V	A1	A2	A3	A4
1	5.98	5.98	3.99	3.12	2.36	9.17	7.08	2.52	1.53
2	5.87	6.34	3.93	2.97	3.03	8.94	7.01	2.43	1.48
3	5.70	6.08	4.15	3.14	2.88	9.19	7.27	2.52	1.58
4	5.69	6.41	4.07	3.22	3.06	9.03	7.53	2.52	1.63
5	5.04	5.35	3.33	2.60	2.24	7.81	5.79	1.98	1.20
6	8.00	8.09	4.78	4.04	3.88	11.54	8.55	2.84	1.77
7	3.87	3.80	2.10	1.59	1.48	5.94	3.90	1.28	0.84
8	6.18	6.61	3.82	3.02	2.49	9.11	6.07	2.04	1.30
9	6.47	6.47	3.95	3.14	2.25	10.64	6.36	2.33	1.35
10	6.07	5.87	3.32	2.37	2.21	9.62	5.49	2.04	1.31
11	4.51	4.20	2.49	2.04	2.04	6.63	4.14	1.53	1.01
12	3.60	3.46	1.85	1.53	1.57	5.25	3.17	1.02	0.67
13	1.22	1.20	0.09	-0.25	-0.17	5.40	2.68	1.00	0.66
14	3.15	2.57	1.46	1.23	1.16	4.32	2.17	0.82	0.63
15	7.43	6.84	4.23	3.45	3.16	11.82	6.32	2.68	1.79
16	5.99	5.64	3.37	2.68	2.60	9.63	5.12	2.02	1.45

Note: I, II, III, IV, and V under the average stress release rate in the table represent the section number shown in Figure 12a, and A₁, A₂, A₃, and A₄ under the average volume release energy represent the calculation area number shown in Figure 13a.

.

4.3.2. Sensitivity Analysis

To reflect the sensitivity of the test indicators to various factors, the range of the average stress release rate and the average volume release energy under each ASRB arrangement scheme obtained from the 16 groups of orthogonal tests mentioned above were calculated. If the range was large, this indicated that the factor has a significant impact on the test index, and vice versa. The range results of each scheme are shown in

Table A1. Sensitivity analysis of the stress release effect of side walls based on stress aspect.

Monitoring Section	Factor Level	Stress Release Effect of Each Factor (%)
		Inclination	Length	Included Angle	Aperture	Spacing
I	1	5.81	4.68	6.12	4.15	6.42
	2	5.77	5.77	5.49	4.45	5.55
	3	5.16	5.38	5.38	5.70	4.63
	4	4.45	5.37	4.21	6.90	4.60
	Range	1.36	1.10	1.91	2.75	1.82
	Influence degree of factors	Aperture > Included angle > Spacing > Inclination > Length
II	1	6.20	4.75	5.98	3.95	6.33
	2	5.96	5.72	5.50	4.59	5.56
	3	5.00	5.23	5.43	5.74	4.71
	4	4.06	5.53	4.32	6.95	4.63
	Range	2.14	0.97	1.66	3.00	1.69
	Influence degree of factors	Aperture > Inclination > Spacing > Included angle > Length
III	1	4.04	2.84	3.66	2.35	3.84
	2	3.51	3.37	3.34	2.58	3.34
	3	2.90	3.24	3.35	3.54	2.72
	4	2.29	3.28	2.40	4.26	2.84
	Range	1.75	0.53	1.26	1.91	1.12
	Influence degree of factors	Aperture > Inclination > Included angle > Spacing > Length
IV	1	3.11	2.15	2.97	1.87	2.99
	2	2.81	2.65	2.64	1.95	2.60
	3	2.27	2.56	2.63	2.70	2.12
	4	1.78	2.61	1.73	3.46	2.27
	Range	1.34	0.50	1.24	1.60	0.88
	Influence degree of factors	Aperture > Inclination > Included angle > Spacing > Length
V	1	2.83	1.67	2.72	1.64	2.56
	2	2.52	2.57	2.50	1.84	2.34
	3	2.02	2.39	2.20	2.48	2.04
	4	1.69	2.43	1.65	3.09	2.13
	Range	1.15	0.90	1.08	1.45	0.52
	Influence degree of factors	Aperture > Inclination > Included angle > Length > Spacing

and

Table A2. Sensitivity analysis of the stress release effect of side walls based on energy aspect.

Monitoring Area	Factor Level	Energy Release Effect of Each Factor (J/m3)
		Inclination	Length	Included Angle	Aperture	Spacing
A1	1	9081.40	8254.90	9242.85	6172.47	9930.12
	2	8598.09	8602.82	8454.61	7517.74	8787.13
	3	8033.13	8395.30	8312.55	9060.52	7843.70
	4	7795.67	8255.27	7498.28	10757.56	6947.34
	Range	1285.73	347.91	1744.57	4585.09	2982.78
	Influence degree of factors	Aperture > Spacing > Included angle > Inclination > Length
A2	1	7223.09	5474.82	6220.69	4080.70	6240.01
	2	6075.19	5804.13	5570.70	4973.82	5594.87
	3	4789.90	5404.53	5467.40	5916.12	5416.65
	4	4070.54	5475.24	4899.91	7188.07	4907.18
	Range	3152.55	399.60	1320.78	3107.37	1332.84
	Influence degree of factors	Inclination > Aperture > Spacing > Included angle > Length
A3	1	2495.17	1957.28	2228.04	1408.79	2319.61
	2	2034.40	2032.40	2025.76	1749.22	2012.70
	3	1731.22	2001.38	1925.57	2139.45	1844.99
	4	1628.37	1898.10	1709.79	2591.70	1711.86
	Range	866.80	134.30	518.25	1182.91	607.76
	Influence degree of factors	Aperture > Inclination > Spacing > Included angle > Length
A4	1	1554.91	1180.99	1440.09	918.26	1482.78
	2	1279.18	1297.90	1284.48	1111.55	1278.68
	3	1084.63	1307.88	1215.00	1384.22	1170.59
	4	1131.97	1263.91	1111.11	1636.66	1118.63
	Range	470.28	126.89	328.98	718.40	364.16
	Influence degree of factors	Aperture > Inclination > Spacing > Included angle > Length

, and the range changes of each factor at different monitoring locations and areas are shown in Figure 15.

From Table A1 and Table A2, and Figure 15, the following conclusions can be drawn. (1) Compared with the calculated results of stress and energy, the two image trends were basically the same, and the laws and change trends of each factor were roughly the same. Similar conclusions were obtained for both angles, thus proving the reliability of the results to a certain extent. (2) By comparing the extreme variation in each factor, it can be seen that on each stress release area fore and aft of the current tunneling head, the order of sensitivity of each factor to the stress release effect was “aperture” > “inclination” > “included angle” > “spacing” > “length” for the most part. According to the order of sensitivity, the arrangement parameters of the corresponding ASRBs can be adjusted to effectively improve the pressure release and energy dissipation effect. (3) Along the TBM advance direction, that is, from I to V in the stress calculation and from A₁ to A₄ in the energy calculation, the sensitivity of various borehole parameters to the stress release effect showed a decreasing trend. In other words, when the ASRB parameters changed, the stress release effect of the rock mass close to the surrounding rock area was greater, while for the area far away from the rock wall, the change in borehole parameters had a smaller impact on the stress release effect.

4.3.3. Correlation Analysis

(1)

Stress aspect

According to the simulation results in Table 9, the average stress release rate results of various factors at different levels and locations are shown in Figure 16. The influence of the “length” factor on the average stress release rate has no obvious rule (Figure 16b). The level of “inclination,” “included angle,” and “spacing” factors were negatively correlated with the average stress release rate (Figure 16a,c,e), while “aperture” was positively correlated (Figure 16d). In addition, along the direction of the tunnel axis, the average stress release rate of each monitoring point showed a decreasing trend, and the average stress release rate of I and II was higher. After reaching III, the stress release effect was significantly reduced.

(2)

Energy aspect

From the perspective of average volume release energy, the simulation results in Table 9 are also plotted, and the average volume release energy results of each factor at different factor levels are discussed, as shown in Figure 17. The conclusions obtained from the analysis of the average volume release energy are basically consistent with the conclusions obtained from the analysis of the average stress release rate. The “length” factor had no significant impact on the average volume release energy (Figure 17b). The level of the “inclination”, “included angle”, and “spacing” factors were negatively correlated with the average volume release energy (Figure 17a,c,e), and “aperture” was positively correlated (Figure 17d). Along the tunnel axis, the average volume release energy of each monitoring point showed a decreasing trend.

4.4. Determination of the Optimal ASRB Layout Plan in Line with Engineering Best Practices

Based on the conclusions of the previous research and analysis, the optimal ASRB arrangement with parameters of 13° in inclination, 33 m in length, 10° in the included angle, 0.26 m in aperture, and 2 m in spacing and the worst ASRB arrangement with parameters of 16.9° in inclination, 30 m in length, 13° in the included angle, 0.2 m in aperture, and 2.6 m in spacing were selected. The results of stress and energy release effects at different locations in the tunnel under the optimal, worst, and average layout schemes are shown in Figure 18. The average stress release rates of the corresponding monitoring points were 8.636% and 1.54%, respectively. The average volume release energies of the corresponding area were 10.00 kJ/m³ and 1.852 kJ/m³, respectively. Compared with the results shown in Table 9, the release effect of the optimal arrangement was better than that seen in the orthogonal test, and the release result of the worst arrangement was worse than that seen in the orthogonal test. Therefore, a correlation between the ASRB parameters and the stress release effect was obtained through the orthogonal test analysis, and the appropriate ASRB parameters were finally determined.

5. Discussion

5.1. Necessity of Parameter Optimization

The program of the maximum principal stress and elastic strain energy distribution under the optimal and worst ASRB arrangements is shown in Figure 19. Under the optimal layout, ASRBs can form a certain range of release areas in the surrounding rock stress concentration area, thus effectively releasing the stress and energy in the surrounding side wall rock and transferring the stress concentration area to the deep part of the rock mass (Figure 19). In the worst arrangement, the release area formed by ASRBs in the stress concentration area was large, but the release effect was not obvious, and the stress concentration area could not be transferred to the deep part of the rock mass (Figure 19).

Similarly, when ASRBs are arranged in the surrounding rock, the surrounding rock stress can be effectively released after the parameters of the ASRB are optimized. However, without parameter optimization, the stress release effect obtained may not be as good as that under the condition that the construction quantities are basically the same. Improper parameters may even lead to unnecessary stress concentrations in the rock mass. Therefore, based on known engineering geological conditions in the study area, it is necessary to conduct correlation and sensitivity analysis on the ASRB layout parameters.

5.2. Method Applicability

It should be noted that the ASRB parameter design method proposed in this paper is based on deeply buried hard rock TBM-constructed tunnels, and a rock deterioration model was used in the numerical simulation of the engineering application process. The conclusions drawn apply only to the conditions defined in this paper, and the relationship between the parameters of ASRB and the parameters of rock mass was not discussed. The design of borehole parameters for ASRBs may vary under different engineering backgrounds, different calculation methods, and calculation conditions. The conclusions and parameter rules drawn in this paper are for reference only. In addition, this study investigated the correlation between ASRB parameters and the effect of stress release and energy dissipation from two levels: the reduction level of maximum principal stress and the reduction degree of strain energy. However, the level of reduction in the degree of kinetic damage in real geologic environments after the implementation of ASRBs and then rockbursts was not investigated in this study, which is a direction for future improvement.

6. Conclusions

The TBM cutting head limits the effective application of SRBs, so carrying out advance stress release has become a key factor in the construction process of deep-buried hard rock tunnels. This paper presents a design methodology for the ASRB parameters in a potential rockburst source area of deeply buried hard rock TBM tunnels, including the test scheme establishment method, parameter selection method, parameter space relationship, and evaluation index establishment method. In addition, the stress release and energy dissipation effects of ASRBs under different arrangement schemes are discussed in detail from the perspectives of maximum principal stress reduction and elastic strain energy release with the background of a deep-buried tunnel project in southwest China. The conclusions are as follows.

(1)

The design method for ASRBs for a deeply buried hard rock TBM tunnel is proposed. This method is based on previous geological data and measured data and comprehensively considers the location of the stress release area and the degree of stress concentration. It can be effectively applied in the design of the layout plan for advance stress release boreholes in the early stage of tunnel construction.

(2)

By comparing the range of each factor in each stress release area fore and aft of the current tunneling head, the sensitivity of the five important design parameters of ASRBs to the stress release effect is, in descending order, “aperture”, “inclination”, “included angle”, “spacing”, and “length”. From the perspective of engineering construction, since the “aperture” parameter is closely related to the on-site drilling equipment and the workload and construction difficulty of on-site construction, it is often difficult to change this parameter. By reasonably optimizing the “inclination”, “included angle”, and “spacing” parameters, the stress release effect can be better improved without increasing the construction workload and instead only optimizing the drilling layout.

(3)

Along the direction of a TBM, the sensitivity of various borehole parameters to the stress release effect shows a decreasing trend. This shows that the stress release effect of the surrounding rock mass close to the TBM can be greatly affected by improving the ASRB parameters, while in the deep rock mass far away from the TBM-constructed area, although there are ASRBs, the release effect is limited by the borehole parameters.

(4)

From the calculation results of each factor, whether from the perspective of the average stress release rate or the average volume release energy, the “length” factor has no significant impact on the pressure release and energy dissipation effect of ASRBs. The levels of the “inclination”, “included angle”, and “spacing” factors have a negative correlation with the stress release effect, while the “aperture” factor has a positive correlation. This shows that under the factor level and simulation conditions set in this study, the layout of “small inclination”, “small included angle”, “small spacing”, and “large aperture” ASRBs often has a better stress release effect than other layouts.

(5)

Along the direction of the tunnel axis, the relationship between the average stress release rate of each monitoring point is I ≈ II > III > IV > V, which shows a decreasing trend along the direction of the TBM. The relationship between the average volume release energy of each area is, in descending order, “A₁”, “A₂”, “A₃”, and “A₄”, which also gradually decreases along the direction of the TBM. This shows that under the simulation environment discussed in this study, the ASRB release area is mainly concentrated in the range of one borehole diameter behind the face.