Numerical and experimental study on optimal design of rock bolts in single-lining support of expressway tunnel

Mengjun Wu; Bolin Jiang; Xuebing Hu; Shanshan Wu

doi:10.1038/s41598-025-24962-0

. 2025 Nov 11;15:39385. doi: 10.1038/s41598-025-24962-0

Numerical and experimental study on optimal design of rock bolts in single-lining support of expressway tunnel

Mengjun Wu ¹, Bolin Jiang ^1,^2,^3,^✉, Xuebing Hu ¹, Shanshan Wu ⁴

PMCID: PMC12606296 PMID: 41219487

Abstract

This study presents comprehensive numerical and experimental investigation into the optimal design of rock bolts in single-lining tunnel support for expressway tunnels. Focusing on key design parameters, including anchorage length, bolt diameter, spacing, surrounding rock grade, and bolt type, the research explores their influence on tunnel stability. The study employs finite element simulations to analyze the distribution of axial force (P_u), surrounding rock stress (s_u), and displacement (d_u). Experimental testing under varying conditions is used to validate the numerical results. The findings reveal that an anchorage length of approximately 2.5 m, a bolt diameter of 28 mm, and an anchorage spacing of 1.0 m offer the best performance for grade III rock conditions. Moreover, self-drilling hollow grouting bolts (SHGB) outperform expansion shell bolts (ESB) in terms of axial force capacity and deformation control. The study concludes by providing practical recommendations for the design of rock bolts in single-lining expressway tunnels, aiming to enhance both safety and cost-effectiveness in tunnel construction.

Keywords: Rock bolts, Tunnel support, Single-lining, Optimal design, Numerical simulation, Experimental testing

Subject terms: Engineering, Solid Earth sciences

Introduction

Tunnel lining systems have undergone significant evolution, progressing from overall linings to composite linings, and more recently to single lining¹. Composite linings, characterized by a sprayed-concrete primary lining combined with a cast-in-place secondary lining and an interposed waterproof layer, have long been the standard in tunnel construction. However, the secondary lining primarily acts as a structural reserve constructed after the surrounding rock deformation has stabilized, which not only reduces its actual contribution to load bearing but also increases cost and prolongs construction schedules. In addition, the multilayer construction sequence complicates rapid excavation and introduces difficulties in ensuring long-term waterproofing reliability^2,3. To overcome these limitations, the concept of single lining has been developed, integrating load-bearing and waterproofing functions within a single structural system, as Fig. 1 shown. This approach promises greater efficiency and economy, but it also imposes more stringent requirements on the primary support, particularly in expressway tunnels where geological conditions are often complex and safety margins are smaller.

Fig. 1 — Comparison between composite and single linings.

In such contexts, rock bolts play a crucial role as the principal reinforcement element of the single-lining support system^4,5. By transferring load between the surrounding rock and the lining, bolts restrain deformation, redistribute stresses, and improve the overall stability of the tunnel⁶. Nevertheless, the mechanical performance of bolts is highly sensitive to design parameters such as anchorage length, bolt diameter, spacing, and bolt type^7,8. Improper parameter selection may result in underutilization of bolt capacity, excessive deformation, or even localized failure^9,10, making parameter optimization essential for both safety and economy in tunnel construction.

Over the past decade, extensive research has been devoted to advancing the understanding of rock bolt behavior. Chen¹¹ developed a combined pull–shear testing approach and demonstrated that D-Bolts exhibit significantly greater displacement capacity compared with conventional rebar bolts, particularly under pull conditions, while also highlighting the influence of joint gaps and host rock strength. Wu¹² carried out static and dynamic Brazilian splitting tests on reinforced sandstone specimens, revealing a two-phase reinforcement mechanism in which bolts initially share tensile loads during the intact stage and subsequently restrain crack propagation once damage occurs, thereby improving residual strength. Pinazzi¹³ examined ungrouted bolts under combined axial–shear loading and reported pronounced reductions in capacity under interaction effects, though the presence of a shear gap alleviated this reduction and improved deformation performance. Chen¹⁴ established and validated an analytical bond–slip model for fully encapsulated bolts, identifying sequential loading phases at the bolt–grout interface and showing that increased grout modulus induces more brittle behavior. Extending these findings, Shokri¹⁵ conducted a systematic review of seventy-seven studies and concluded that three factors—rock mass and boundary conditions, grout mechanical behavior, and bolt geometry—are the dominant controls on axial load transfer. More recently, Ma¹⁶ investigated system bolts in shallow four-track high-speed railway tunnels, introducing a deformation pressure theory framework and showing that long–short combined bolt schemes could reduce axial forces and deformations by over 70% in Class V rock, thereby offering practical optimization strategies. Focusing the long-term corrosion damage, Wu’s studies^17–19 have revealed that cable bolts may suffer durability degradation, stress corrosion cracking, and hydrogen-assisted fracture under coupled underground environments .

Together, these studies have deepened knowledge of bolt mechanics under diverse loading conditions, clarified reinforcement mechanisms, and introduced analytical and experimental tools for design. However, most prior works have focused on either specific loading scenarios, individual parameter effects, or particular structural contexts such as mining excavations or railway tunnels. Few have systematically evaluated the combined influence of multiple bolt parameters within the setting of single-lining expressway tunnels, where the support must simultaneously serve as both temporary and permanent lining under highly variable geological conditions.

Addressing this gap, the present study combines numerical simulation with experimental testing to investigate the influence of anchorage length, bolt diameter, spacing, surrounding rock grade, and bolt type on the performance of rock bolts in single-lining tunnel support. By analyzing the distribution of bolt axial force (P_u), surrounding rock stress (s_u), and displacement (d_u), the study establishes a comprehensive basis for parameter optimization. Distinct from previous research, this work not only evaluates multiple parameters in an integrated framework but also emphasizes their application to the unique challenges of single-lining expressway tunnels. The findings aim to provide both theoretical insights and practical recommendations for safer and more economical tunnel support design.

Engineering case

Geological conditions

This study is based on the single-layer lining support project of a highway tunnel located in Sichuan Province, China. The target tunnel section is situated at an elevation of 500–1000 m, with a relative height difference of 300–600 m. The terrain is characterized by moderate lateral slopes, and locally exposed hard rock zones exhibit moderately steep morphology, typical of a mid- to low-mountain region. The tunnel reaches a maximum burial depth of 1270 m and crosses the Chengqiangyan anticline. Its alignment is nearly orthogonal to the structural trend and intersects the maximum horizontal principal stress at a small angle. The strata comprise a variety of lithologies. According to rock strength, rock mass structure, and degree of integrity, the portal section is mainly classified as Grade III–V surrounding rock. Based on the groundwater occurrence and hydrogeological characteristics in the tunnel area, the aquifer types are divided into three categories: loose pore water, karst water, and bedrock fissure water. Figure 2 shows the geological cross-sectional view of the target tunnel construction.

Fig. 2 — Geological cross-sectional of target tunnel.

Tunnel conditions

The excavation method varied according to the surrounding rock grade. For Grade III surrounding rock, the full-section excavation method was adopted, employing handheld pneumatic drills in combination with the smooth blasting technique. For Grade IV surrounding rock, a three-bench excavation method (upper, middle, and lower benches) was applied, mainly using mechanical equipment and handheld pneumatic picks. Excavation was generally performed without blasting, while auxiliary weak blasting was adopted only when necessary to minimize disturbance to the strata. In deeper sections with hard rock, the upper–lower bench method with reserved core soil served as the primary tunneling approach. For Grade V surrounding rock, the three-bench method with reserved core soil was employed, primarily relying on manual pneumatic picks without blasting; when required, pre-splitting and micro-vibration blasting were adopted as supplementary measures. Figure 3 illustrates the tunnel section and its dimensions, with the single lining support thickness of 0.26 m.

Fig. 3 — Illustration of tunnel section.

The physical and mechanical parameters of rocks and supports were obtained through field sampling and laboratory testing (Fig. 4), as detailed in Table 1.

Table 1.

Material properties of surrounding rock and support.

Material	E (GPa)	μ	γ (kg/m³)	c (MPa)	φ (°)	σ_ci (MPa)	σ_cm (MPa)
Rock grade III	13	0.275	2550	0.97	34	20.1	3.6
Rock grade IV	4	0.325	2350	0.62	30	8.3	2.2
bolt	200	0.25	7500	-	-	-	-
Shotcreting	32	0.2	2500	2.94	50	-	-

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In Table 1, E denotes the modulus of elasticity, μ denotes the Poisson’s ratio, γ denotes the density, c denote rock cohesion, φ denotes the internal friction angle; the uniaxial compressive strength of intact rock (σ_ci) was obtained from laboratory tests, while the equivalent uniaxial compressive strength of the rock mass (σ_cm) was obtained from site in-situ tests.

Numerical simulation and discussion

Model description

Model establishment

The numerical simulation is conducted using Abaqus, a finite element software widely employed for underground engineering analysis. The tunnel section of established numerical model bases on the geological conditions of tunnel construction, with additional considerations on lining thickness, reserved deformation, and extension of reserved reinforcement space. The Mohr–Coulomb constitutive model is employed in this simulation. For surronding rock, it is designed to be 70 m in width and 100 m in height, as Fig. 5a shown. The shotcrete lining and rock bolts are represented as structural elements, with the bolts modeled as embedded truss elements^8,20,21. The anchorage of bond bolt (Self-drilling Hollow Grouting Bolt, later utilized in physical tests) is simulated as full interfacial bonding to surrounding rock along the axial direction, while the anchorage of mechanical bolt (Expansion Shell Bolt, later utilized in physical tests) is simulated as concentrated force at the bolt end.

Fig. 5 — Numerical simulation: (a) Model, and (b) Boundary conditions.

The number of simulation tunnel sections, bolt arrangement, simulation conditions, etc., comply with the experimental tests, which is introduced later in this paper. The mechanical properties of the surrounding rock, shotcreting, and rock bolt employed for numerical simulation are defined based on engineering condition and laboratory test results, complys with Table 1.

Boundary condition and excavation simulation

The model incorporates a full tunnel cross-section with realistic boundary conditions, as Fig. 5b shown. The in-situ stress as 1.10 MPa, obtained from field measurements, was applied through a geostatic initial stage: gravity loading was first imposed, followed by prescribing the measured vertical and horizontal stress values as initial stress conditions. Static equilibrium was confirmed before proceeding to excavation simulation.

The stress release complys with the stages of excavation procedures, which are listed in Table 2. The excavation is carried out in full-face mode, following the sequence of excavation, installation of rock bolts, and shotcrete (single-layer lining). The analysis is divided into three steps: excavation, rock bolt installation, and lining. Each analysis step has a step size of 1, with a minimum step size of 0.1. Six calculation steps are performed for each analysis step.

Table 2.

Excavation stages of numerical simulation.

Construction step	Work	Stress release
1	Self-weight	0
2	Excavation	60%
3	Bolt installtion	80%
4	Shotcreting	100%

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Disucssion on numerical results

To better evaluate the support effect of rock bolts to single lining tunnel, three key indicators are introduced and discussed via the results^21,22: maximum axial force in bolts P_u, maximum stress of surrounding rock s_u, and maximum displacement of surronding rock d_u. The simulation results indicate that there are common patterns of P_u, s_u, d_u between different test conditions. To avoid the influence of edge effect, the following discussion bases on the simulation result of the middle section along the tunnel direction, as Fig. 6 shown.

Fig. 6 — Simulation result patterns under primary group.

Figure 6 shows the common pattern of simulation result distribution under primary group condition (refers to Table 3). The bolt embedded at the tunnel crown generally experiences a maximum axial force P_u. The maximum stress in surrounding rock s_u generally appears at the tunnel crown, while the maximum displacement of surrounding rock d_u generally appears at the tunnel springline.

Table 3.

Test results.

Group	Test number	l (m)	d (mm)	s_l × s_c (m × m)	Surrounding rock grade	Bolt type
Primary	1	2	25	1 × 1	III	SHGB
Anchorage length	2	1.5	25	1 × 1	III	SHGB
	3	2.5	25	1 × 1	III	SHGB
	4	3	25	1 × 1	III	SHGB
Bolt diameter	5	2	22	1 × 1	III	SHGB
	6	2	28	1 × 1	III	SHGB
	7	2	30	1 × 1	III	SHGB
Longitudinal spacing	8	2	25	0.8 × 1	III	SHGB
Longitudinal spacing	9	2	25	1.2 × 1	III	SHGB
Circumferential spacing	10	2	25	1 × 0.8	III	SHGB
Circumferential spacing	11	2	25	1 × 1.2	III	SHGB
Surrounding rock grade	12	2	25	1 × 1	IV	SHGB
Bolt type	13	2	25	1 × 1	III	ESB

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The common distribution patterns of P_u, s_u, d_u comply with the findings from other researches^23–25, and the simulation results provide the benchmark for the design of experimental program. The values obtained from the numerical simulation are discussed and validated later in the comparison of numerical and experimental results (Table 4).

Table 4.

Test results.

Test number	P_u (N)	P_n/r_d (N/%)	s_u (MPa)	s_n/r_d (MPa/%)	d_u (mm)	d_n/r_d (mm/%)
1	3589	3390/5.5	0.43	0.39/9.3	0.009	0.0083/7.8
2	3485	3130/10.2	0.45	0.41/8.9	0.012	0.0114/5.0
3	3989	3425/14.1	0.42	0.38/9.5	0.008	0.0076/5.0
4	4000	3480/13.0	0.41	0.36/12.2	0.007	0.0067/4.3
5	3405	2920/14.2	0.45	0.41/8.9	0.012	0.0107/10.8
6	4012	3575/10.9	0.41	0.38/7.3	0.007	0.0062/11.4
7	4223	4065/3.7	0.39	0.36/7.7	0.006	0.0053/11.7
8	3703	3480/6.0	0.42	0.38/9.5	0.007	0.006/14.3
9	3472	3280/5.5	0.46	0.42/8.7	0.011	0.0104/5.5
10	3615	3430/5.1	0.42	0.38/9.5	0.008	0.0071/11.3
11	3508	3345/4.6	0.45	0.40/11.1	0.010	0.0087/13.0
12	3912	3550/9.3	0.46	0.41/10.9	0.010	0.0092/8.0
13	3200	2780/13.1	0.47	0.44/6.4	0.013	0.0117/10.0

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In Table 4, P_n, s_n, d_n denote the numerical results on the maximum bolt axial force, the maximum surrounding rock stress, the maximum surrounding rock displacement, respectively, while r_d denotes the difference ratio from the experimental results to the numerical results.

Experimental program

Test design

Test conditions

To obtain a comprehensive understanding on the supporting effect of rock bolts in single lining tunnel, this paper investigates the influences of following parameters via experimental program: the anchorage length l, the bolt diameter d, the anchorage spacing (in longitudinal and circumferential directions), surrounding rock grade, and the bolt type.

The test condition designs on l, d, s_l (the longitudinal anchorage spacing), and s_c (the circumferential anchorage spacing) comply with the common engineering constrcution in practice. The experimental tests are conducted with the tunnel segments under surrounding rock grade III-IV.

The bolt types utilized in engineering construction are generally determined by surrounding rock condition²⁶. For this paper, the Self-drilling Hollow Grouting Bolt (SHGB) and the Expansion Shell Bolt (ESB) are employed for experimental testing, as Fig. 7 shown.

Fig. 7 — Rock bolts: (a) SHGB, and (b) ESB.

A total of 13 test conditions are conducted using an orthogonal design matrix to reduce computational workload while ensuring coverage of major interactions. Table 3 shows the test conditions of experimental program.

Anchorage arrangement

The experimental testing contains nine sections of bolt support for each test condition, and the tunnel longitudinal bolts are arranged in a staggered pattern²⁷, with a longitudinal spacing s_l between tunnel sections, as Fig. 8 shown.

Fig. 8 — Anchorage arrangement and measurement.

The tunnel circumferential bolts are embedded in the anchorage spacing of s_c, with central symmetrically arranged. For each tunnel section, in total 19 or 20 (depending on the staggered arrangement) rock bolts are installed. As Fig. 8 shown, in the nine tunnel sections, 19 rock bolts are installed for tunnel sections with odd order (the anchorage arrangment is marked by solid lines), while 20 rock bolts are installed for tunnel sections with even order (the anchorage arrangment is marked by dash lines).

Installation and measurement

Installation

The installation of rock bolts is conducted via a drilling machine to gurantee the embedment depth and drilling verticality, as Fig. 9 shown. The installation procedure of rock bolts follows a order of bolt anchorage, grouting, shotcreting. The anchorage length and the grouting compaction degree are qualified by a rock bolt non-destructive tester after the grout reachs the target strength.

Measurement

To eliminate the edge effect on test results, the experimental testing conducts within the middle tunnel section (the fifth order section in the nine sections). The bolt axial force, stress and displacement in surrounding rock are measured via bolt load cells (three for each rock bolt), rock stress meters, convergence meters, respectively, as Fig. 10 shown. The measurement location and placement refer to the numerical results, as detailed in Fig. 8.

Fig. 10 — Measurement devices: (a) Bolt load cell, (b) Rock stress meter, and (c) Convergence meter.

Comparison of numerical and experimental results

There are similar distribution patterns between the experimental results and the numerical results for all the test condition cases: the maximum bolt axial force P_u occurs in the bolt embedded at the tunnel crown, the maximum stress of surrounding rock s_u appears at the tunnel crown, and the maximum displacement of surrounding rock d_u appears at the tunnel springline. The Table 4 shows the comparison between the values obtained from numerical simulation and experimental testing.

From Table 4, the difference ratio r_d from the experimental results to the numerical results is less than 15%, validating the accuracy and reliability of the discussion and conclusion obtained from the numerical simulation in this paper.

Discussions on key parameter influences

This paper discussed the influences of key parameters on the rock bolt support effect based on the results obtained from experimental testing, as follows.

Anchorage length

Based on the results from group primary and group anchorage length, Fig. 11 shows the variation of P_u, s_u, d_u with the increasing anchorage length.

The experimental results show P_u increases with the increasing anchorage length, with a varying ascending slope. The growth percentages from (1.5–2.0) m, (2.0–2.5) m, (2.5–3.0) m are 3.0%, 11.1% and 0.3%, respectively, as marked in Fig. 11a. There occurs the greatest increase of P_u when the anchorage length increases from 2.0 m to 2.5 m (about 11.1%), and P_u hardly grows under an anchorage length greater than 2.5 m, indicating a growth limit of anchorage length influence on P_u.

Regarding the maximum stress s_u and displacement d_u in surrounding rock, they decrease with the increasing anchorage length. There is a significant improvement on support effect when the anchorage length increases from 1.5 m to 2.0 m. However, the changing ratios indicate a weaken effect on rock bolt support when the anchorage length is greater than 2.0 m.

Bolt diameter

Based on the results from group primary and group bolt diameter, Fig. 12 shows the variation of P_u, s_u, d_u with the increasing bolt diameter.

The experimental results show P_u increases with the increasing bolt diameter, with the ascending ratio of 5.4%, 11.8%, 5.3%, when the bolt diameter increases from (22 to 25) mm, (25 to 28) mm, (28 to 30) mm, respectively. A greater improvement of support effect can be observed when the bolt diameter increases from 25 to 28 mm.

Regarding the s_u and d_u, they decrease with the increasing bolt diameter. The descending ratios between the different bolt diameter gaps are roughly equal, indicating an approximate linear effect of bolt diameter on support effect.

Anchorage spacing

Based on the results from group primary, group longitudinal spacing and group circumferential spacing, Fig. 13 illustrates the variation of P_u, s_u, d_u under different anchorage spacing conditions, considering both longitudinal and circumferential spacing. The experimental results indicate that P_u decreases as the spacing increases, whereas s_u and d_u generally increase. This confirms that denser bolt arrangements enhance axial load utilization and effectively restrain stress concentration and deformation in the surrounding rock.

From Fig. 13a, the changing ratios when the anchorage spacing increases from (0.8 to 1.0) m are 3.1% (for s_l) and 0.7% (for s_c), from (1.0 to 1.2) m are 3.3% (for s_l) and 2.3% (for s_c), indicating that the increasing anchorage spacing has less influence on P_u when the anchorage spacing is greater than 1.0 m. For s_u, compared with the increase ratio when the anchorage spacing increases from 0.8 m to 1.0 m (2.4% for s_l and s_c), there is a significant increase when the anchorage spacing increases from 1.0 m to 1.2 m (7.0% for s_l and 4.7% for s_c). While the experimental results show the anchorage spacing has an approximate linear influence on the changes of d_u.

However, the comparison on the influences of longitudinal and circumferential spacing shows the changing ratios under the increasing circumferential spacing are generally smaller than those under the increasing longitudinal spacing. This indicates the support effect of rock bolts behaves less sensitively to the changes of circumferential spacing, compared to the longitudinal spacing.

Surrounding rock grade

Based on the results from group primary and group surrounding rock grade, Fig. 14 presents the comparison of P_u, s_u, d_u between Grade III and Grade IV surrounding rocks. The results indicate that the supporting performance of rock bolts deteriorates in weaker geological conditions.

Specifically, P_u increases by approximately 9.0% when the rock grade changes from III to IV, indicating a more complete utilization of bolt capacity under the poorer surrounding rock condition. Even though, the results clearly show the surrounding rock occurs a higher stress concentration and greater deformation: s_u, and d_u both increase under Grade IV conditions by about 7.0% and 11.1%, respectively.

Bolt type

Based on the results from group primary and group bolt type, Fig. 15 shows the experimental results comparing Self-drilling Hollow Grouting Bolts (SHGB) with Expansion Shell Bolts (ESB).

The results indicate that SHGB generally provides superior performance. The maximum bolt axial force P_u of SHGB is about 10.8% higher than that of ESB under identical conditions, due to the continuous bonding achieved through grouting^28,29. In contrast, ESB relies on point anchorage, which is more sensitive to rock integrity and less effective in fractured rock mass.

For the surrounding rock stress s_u and displacement d_u, SHGB consistently achieves lower s_u and d_u values compared with ESB. Specifically, s_u is reduced by approximately 8.5%, while d_u decreases by about 30.8% when using SHGB.

These results demonstrate that SHGB not only performs a more efficient utilization on bolt capacity but also a better control on stress concentration and significantly, on deformation in surrounding rock. ESB, while still functional, shows a weaker support effect to the surrounding rock under the surrounding rock condition of Grade III.