Based on the theory of wave dynamics, this study systematically derives the steady-state analytical solution for the scattering of plane SV-waves by composite lined tunnels in an infinite space using the wave function expansion method. On this basis, a theoretical calculation model for circular composite linings under blast loading is established. Based on the steady-state analytical solution, the δ(x)-function and the Heaviside step function are introduced to construct the Duhamel integral, transforming the transient wave problem into an integral form. By further incorporating the Fourier integral transform, an analytical solution for the transient response around a composite lining tunnel subjected to a plane blast SV wave is ultimately derived. The computational results of this study are subsequently validated against those reported in existing literature. On this basis, a systematic investigation was conducted into the influence of parameters such as blast loading duration, lining thickness, and elastic modulus on the transient dynamic stress concentration factor (DSCF) of the tunnel, incorporating engineering data from the Hongshan South Road tunnel group. The results indicate that the DSCF values in the secondary lining of the composite tunnel are greater than those in the surrounding rock. The elastic moduli of both the surrounding rock and the secondary lining have a significant influence on the DSCF of the lining. Therefore, under the premise of ensuring adequate stability of the surrounding rock, materials with lower stiffness should be preferentially selected for the secondary lining. Increasing the thickness of both the surrounding rock and the secondary lining can markedly reduce the DSCF within the lining. The analytical results can provide a theoretical basis for the anti-blast design of tunnels.

This paper presents an analytical solution for near-field cylindrical P-wave scattering by a circular tunnel. A comprehensive elastic–slip interface model is incorporated to capture localized discontinuous deformations and frictional sliding. Employing the wave function expansion method and Graf’s addition theorem, the dynamic stress concentration factor (DSCF) of both soft and stiff linings is systematically investigated. The results reveal that near-field wavefront curvature severely amplifies stress concentration on the illuminated side, degenerating into a plane-wave response only when the dimensionless source distance exceeds 50. Furthermore, within the parameter range considered, the imperfect interface exhibits a dual “flexible barrier” effect heavily influenced by impedance matching: it tends to act as a seismic isolator that reduces the DSCF for stiff linings, but can weaken boundary confinement and exacerbate stress concentration for soft linings. These findings provide crucial theoretical insights for the blast-resistant design of underground structures.

Blasting-induced vibrations from new tunnel construction pose a significant threat to the structural safety of existing tunnel linings due to dynamic stress concentration. To address this, this study establishes a transient-response analytical model for composite lining tunnels using wave function expansion and a combination of the Duhamel integral and Fourier transform methods. Through a case study of the Hongshan South Road Tunnel, the research systematically quantifies the influence of critical factors such as load rise time, lining thickness, and material stiffness. Numerical results reveal that under blasting P-wave action, the inner vault of the secondary lining exhibits the most significant dynamic stress concentration, identifying it as the primary vulnerable zone. Furthermore, peak dynamic stress and vibration velocity increase sharply as the load rise time decreases, indicating that short-duration, high-intensity impacts present the greatest hazard. To mitigate these effects, the study identifies several optimization strategies: increasing the thickness of the initial support and employing high-modulus materials effectively reduce stress peaks. Specifically, maintaining the elastic modulus ratio of the surrounding rock to the initial support at approximately 2.0 provides an optimal balance for enhancing blast resistance. The findings suggest that tunnel design should prioritize optimizing the stiffness of the initial support and utilizing grouting to reinforce the surrounding rock. This research provides a robust theoretical framework and specific parameter optimization directions for the seismic and blast-resistant design of composite lining tunnels.

Grounded in the principles of wave dynamics, this study employs the wave function expansion approach to mathematically describe how plane P- and SV-waves scatter around a composite tunnel lining embedded in an unbounded medium. To establish the transient analytical framework for the dual-layer structure subjected to blast excitations, we integrate Fourier integral transforms alongside the Heaviside step and Dirac delta functions. We systematically analyze how the tunnel’s transient dynamic stress concentration factor (DSCF) responds to variations in the shear modulus ratio, as well as the specific characteristics of the incoming waves (i.e., wave type and dimensionless pulse duration). Furthermore, a seismic mitigation strategy featuring a “soft-exterior, rigid-interior” configuration is theoretically explored. The analytical outcomes theoretically indicate that short-duration transient waves provoke severe dynamic stress concentrations within the lining, with SV-waves posing a markedly greater threat to structural integrity than P-waves. Analyses reveal that the peak dynamic stress concentration (DSCFmax) primarily localizes at the tunnel’s crown and invert. Interestingly, altering the pulse duration does not significantly shift this spatial distribution pattern. Ultimately, analytical results suggest that adopting the “soft-exterior, rigid-interior” design and optimizing the thickness of the primary support can substantially alleviate these stress concentrations, providing preliminary theoretical guidance for vibration attenuation.