Aug 2026· International Journal of Applied Mechanics· 0 citations
Abstract
During tunnel construction in weak strata, the coupled effects of ground rheological behavior and stress release significantly influence both construction progress and safety. As a critical support measure in tunneling engineering, the time-dependent mechanical interaction between rock bolts and the surrounding rock under such complex conditions remains insufficiently understood. To elucidate the time-dependent interaction mechanism between rock bolts and surrounding rock under these challenging engineering conditions, this study develops an analytical solution for bolted tunnels that explicitly couples tunnel excavation-induced stress release and ground rheology. The rheological behavior of the ground is characterized using classical Maxwell and Kelvin-Voigt creep models, while the stress release effect is represented through the virtual support pressure method. A closed-form analytical solution is ultimately derived via integral transforms. The solution accounts for two types of rock bolts: end-anchored rock bolts and fully grouted rock bolts, which are distinguished by modifying the contact conditions at the boltrock interface. Numerical simulations verify the validity and engineering applicability of the proposed analytical method. Furthermore, parametric studies are conducted to examine the influence of bolt parameters and stress release parameters on surrounding rock deformation. The proposed analytical approach provides researchers and engineers with an improved theoretical understanding of the interaction between rock bolts and tunnel surrounding rock in weak strata.
High-stress soft rock roadways in deep underground engineering often exhibit significant time-dependent deformation due to strong rheological behavior of surrounding rock. To investigate the deformation characteristics and support effect, a composite viscoelastic constitutive model considering anchored and unanchored rock zones is established based on the Maxwell rheological framework. The equivalent stiffness contribution of rock bolts is incorporated to characterize the interaction between support and surrounding rock. Analytical solutions of radial displacement and creep rate are derived using viscoelastic theory and Laplace transform methods. The effects of bolt spacing, bolt length, and burial depth on the rheological response are analyzed. Numerical simulations based on FLAC3D creep analysis and field monitoring data are used to verify the proposed model. Results show that decreasing bolt spacing effectively reduces long-term deformation, while bolt length has a diminishing effect beyond a critical anchorage length. Increasing burial depth significantly increases creep rate and total deformation. The numerical results agree well with theoretical predictions (R2 ≈ 0.985), and field measurements show a relative error within 10%. The proposed model effectively describes the long-term deformation trend of high-stress soft rock roadways and provides a theoretical reference for support design under similar conditions.
Yongsheng Han, Shulin Lu, K. Guo et al.· Applied Sciences· 0 citations
The interactive mechanism between the surrounding rock and lining system is a central issue in tunnel-support design. Previous studies have seldom considered both the hardening characteristics of the shotcrete lining and the intermediate principal stress effect simultaneously, resulting in inaccurate predictions of tunnel convergence and support pressure. To address this, a coupled analytical model for rock–lining interaction is developed based on the Kelvin–Voigt model and unified strength theory. This model characterizes the shotcrete hardening process through its time-evolving stiffness and represents the tunnel-face confinement effect using the concept of fictitious support pressure. The accuracy and reliability of the coupled analytical solutions are verified by comparing them with field-monitoring data. Furthermore, the effects of relevant parameters on the mechanical performance of tunnel structures are analyzed through a case study. The results show that neglecting the hardening characteristics of the shotcrete lining leads to an underestimation of tunnel convergence but an overestimation of the pressure borne by the shotcrete lining. Accounting for the intermediate principal stress unlocks the self-supporting potential of the rock, resulting in optimized support parameters and lower construction costs. An increase in the creep modulus parameter (
G
2
) leads to a reduction in tunnel wall deformation; consequently, the support pressure also decreases. As the excavation speed increases, the stress release rate increases, leading to greater tunnel wall deformation and higher support pressure. With increases in the creep modulus parameter (
G
2
) and excavation speed, the development of the viscoplastic zone in the surrounding rock accelerates. These findings provide a theoretical foundation for support design and construction in similar tunnel projects.
Zhixiong Peng, Yani Lu, Yawu Zeng et al.· International Journal of Geo...· 0 citations
A single corrosion pit in a grouted rockbolt should be mechanically interpreted as a localized weakened segment, because it introduces a discontinuity in axial stiffness, disturbs the dominant load-transfer zone near the loaded end, and complicates the ultimate failure behavior of the anchorage system. To clarify this mechanism, a three-segment analytical model is developed, in which the pit-corroded portion is equivalently represented as a locally weakened segment between two intact segments. Under the assumptions of compatible axial deformation between the rockbolt and grout and linear shear transfer at the grout-rock interface, analytical solutions for axial displacement, total axial force, and interfacial shear stress are derived using the state vector and transfer matrix method. The model is validated by numerical simulation and then used to investigate the effects of pit geometry, material modulus degradation, and external load-transfer parameters. The results show that the principal effect of a single corrosion pit is the disturbance of the front-segment load-transfer zone caused by local stiffness reduction, leading to the redistribution of displacement, axial-force attenuation, and interfacial shear-stress evolution. Among the corrosion-related parameters, pit length and material modulus degradation exert the strongest influence on response deterioration, whereas pit depth mainly governs the local fracture susceptibility of the weakened segment. Two ultimate bearing-capacity criteria are further established for interface slip-debonding and weakened-segment fracture, and the final bearing capacity is determined by the competition between these two failure modes. This study provides a mechanistic basis for the assessment of locally pit-corroded grouted rockbolts.
Xiang Xu, Shuqi Ma, Jiazheng Chen et al.· Engineering Research Express· 0 citations
In deep roadways with soft surrounding rock, the anchorage section of conventional cylindrical rock bolts relies on the bonding and friction at the interface between the anchoring agent and the surrounding rock for load transfer, which is prone to issues such as localized stress concentration in the anchoring agent, rapid development of plastic damage in the surrounding rock, and interface debonding failure. These problems make it difficult for the ultimate anchoring force of the bolt to meet the support requirements under high in-situ stress conditions. This study systematically quantifies the coupling relationship among the 40° wedge-shaped reaming length, anchoring force, and surrounding rock damage. A three-dimensional bolt–anchoring agent–surrounding rock numerical model was established using ABAQUS. With the wedge-shaped reaming angle fixed at 40°, five groups of reaming length conditions—4 cm, 6 cm, 8 cm, 10 cm, and 12 cm—were set up for uniaxial pull-out simulations to reveal the strengthening mechanism of 40° wedge-shaped reaming anchorage. The simulation results reveal that reaming length plays a significant role in modulating the mechanical state of the anchoring system. For short reaming lengths (4–6 cm), the reinforcement effect remained limited and the anchoring agent stress was highly localized near the wedge tip. In the medium range (8–10 cm), the stress within the anchoring agent became more evenly distributed over the anchorage length, while plastic damage in the surrounding rock remained dispersed and non-interconnected; under these conditions, the bolt anchoring force showed the largest improvement, exceeding that of conventional straight-hole bolting by more than 42%. Once the reaming length surpassed 10 cm, the plastic zone in the surrounding rock became interconnected and softened, and the incremental gain in anchoring force diminished markedly. Based on the mechanical response and overall load-bearing performance of the system, 10 cm is identified as the optimal reaming length for the 40° wedge-shaped configuration. These results provide a quantitative reference for designing high-pressure water-jet reaming parameters in deep soft-rock roadways.
Jie Chen· International Journal of Ene...· 0 citations
Underground railway systems provide a vital solution to urban spatial constraints, yet their construction in weak rock formations poses severe geotechnical challenges. Issues such as ground settlement and tunnel deformation under dynamic train loads can compromise structural integrity and operational safety. This study addresses these complexities by integrating a novel two-dimensional Finite Element model with a complementary viscoelastoplastic analytical framework. This dual approach effectively correlates global dynamic responses with localised continuum effects. A detailed parametric study reveals that axle loads exert a more pronounced effect on the track structure than the tunnel lining, increasing track displacement by 23.9% compared to only 12.3% for the lining. At high operational speeds, the numerical analysis identifies a stability plateau attributed to radiation damping, while the analytical model predicts a conservative upper-bound response. The analysis further demonstrates that increasing the Young’s modulus of the surrounding rock beyond 1000 MPa reduces vertical displacement to negligible levels. Geometrically, while circular cross-sections offer superior radial confinement, they exhibit an 18.5% increase in localised invert settlement compared to horseshoe profiles due to a punching shear mechanism. By establishing a mechanical hierarchy, this study provides engineers with a strategy to use analytical methods for safety baselines and numerical modelling for realistic serviceability limits.
Hafsa Farooq, Sanjay Nimbalkar· Geotechnical and Geological...· 0 citations
Fully grouted rock bolts are widely used for ground control in underground excavations and slopes. Their behaviour under axial and shear loading is governed by bond-slip at the interfaces, confinement, embedment length, annulus thickness and bolt profile, which together control peak capacity and post-peak load transfer. Although many studies have examined individual aspects of this behaviour, a consolidated assessment of axial and shear load-transfer mechanisms remains limited. This review addresses that gap by systematically reviewing Scopus-indexed literature from 1988 to 2025. An initial broad search returned 977 records on rock-bolting systems. After applying focused search terms, exclusions and manual screening, 122 articles were selected for detailed bibliometric and content-based analysis. VOSviewer keyword mapping identified three main research clusters: (a) grout, pull-out testing,analytical modelling, shear stress, and shear strength; (b) finite-difference modelling and failure mechanisms; and (c) numerical simulation using the finite element method. The review also compares publication trends, leading contributors and the main technical themes shaping the field. . The findings revealed that the axial behaviour is mainly bond-controlled, whereas joint conditions, boundary constraints, and local bending more strongly influence shear behaviour. These differences highlighted the need for careful interpretation of test data and for modelling approaches that distinguished between the axial and shear load transfer mechanisms in fully grouted rock bolts.
Shima Entezam, A. Mirzaghorbanali, B. J. Shokri et al.· Australian Geomechanics Jour...· 0 citations