## 5 Conclusions  
Based on [PERSON]'s short cylindrical cavity solution, this study derives an analytical model for dynamic stresses in the surrounding rock of adjacent tunnels by incorporating the axial pressure \(q(t)\) generated by instantaneous detonation and the rock mass damage factor D. A case study was conducted to investigate stress magnitudes and propagation behavior, with validation through field measurements. The theoretical stress values derived from the model show consistent trends and minor numerical deviations when compared to measured data. 1. Stress magnitude and propagation laws: Both theoretical and measured results exhibit consistent triaxial stress trends in the following order: radial stress > axial stress > hoop stress. All three stresses decrease with increasing distance and damage factor, showing an inverse relationship with distance. Radial stress decays at the highest rates, followed by axial and hoop stresses. Stress also decays exponentially over time, with the peak occurring after the arrival of the transverse S-wave. 2. Advantages of proposed stress model: Incorporating instantaneous detonation pressure significantly improves accuracy compared to conventional models that neglect this factor, reducing average errors by 11.25% in radial stress and 9.68% in axial stress. Including the damage factor D reveals nonlinear stress attenuation with increasing damage. At D = 0.4, compared to the intact rock condition (D = 0), stress reductions  
Figure 25: Comparison between measured and theoretical values of stress. reach 44.58% (radial), 29.55% (axial), and 27.18% (hoop), confirming the importance of accounting for detonation pressure and rock mass damage in stress prediction. 3. Validation through field measurements: Measured stresses show small deviations from theoretical values, with average errors of 7.02% (radial), 7.56% (axial), and 7.05% (hoop). This close agreement validates the reliability of the proposed analytical solution. Note: The primary limitations of the stress calculation model in this study are its initial assumption of heterogeneous, anisotropic rock masses as homogeneous media, with stress computed through the introduction of a damage factor. This elasticity-based model simplifies reality and does not fully capture the complex behavior of anisotropic rock. In practice, stress wave propagation in such media is nonlinear, and influenced by transmission, refraction, and reflection at rock mass discontinuities, as well as strain-softening effects in tunnel rock [45]. During multi-borehole stress superposition, the rock between the cut holes and the central pillar is treated as a continuous medium. However, auxiliary (relief) and perimeter pilot holes cause additional stress attenuation due to wave scattering at these cavities. To address these limitations, future research will focus on the following: (1) Stress wave propagation in anisotropic and fractured rock masses using a true triaxial Hopkinson bar system to simulate in situ stress conditions, and ultrasonic transmission techniques to monitor P-wave velocity evolution under varying stress paths [46]. (2) Discrete element modeling (DEM) to simulate contact mechanics across rock discontinuities. (3) Numerical simulation tools to study stress wave behavior in rock masses containing pre-existing cavities. These approaches aim to improve theoretical accuracy and better reflect real-world conditions. Methodology, T.L., X.L. and X.H. ; resources, Y.H. and Y.X. ; data curation, Y.W., J.Z., Y.H. and Y.X. ; writing--original draft, Y.W. and J.Z. ; writing--review and editing, T.L., X.L. and X.H. ; funding acquisition, T.L. All authors have read and agreed to the published version of the manuscript. This work is supported by the Xiaoming Lou: Natural Science Foundation of China (No. 52109124). Not applicable. The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.