Abstract
The modulus of subgrade reaction is a key parameter used in tunnel design. However, the existing analytical relations for determining the modulus mainly focus on deep tunnels in the homogeneous ground. Therefore, the complex variable method was used to develop analytical solutions for calculating the modulus of subgrade reaction for deep circular tunnels close to bedrock and shallow circular tunnels under uniform and oval deformation patterns. Subsequently, the analytical solutions were validated by comparing them with numerical solutions. At last, parametric studies were conducted to analyze the impacts of the bedrock and ground surface on the modulus of subgrade reaction. The results show that the modulus increases substantially near the bedrock and decreases slightly away from the bedrock, while the ground surface has the opposite effect. In addition, the effects of the bedrock and the ground surface on the radial modulus are more significant than that on the tangential modulus. Furthermore, the results confirm the effect of the tunnel deformation pattern on the modulus of subgrade reaction. The analytical solutions may be used for obtaining the approximate magnitude of the modulus of subgrade reaction in the structure design of shallow tunnels and deep tunnels close to bedrock.
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This work was supported by the National Natural Science Foundation of China (Grant numbers 52079134, 51991393).
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Zhao, W., Xie, P., Chen, W. et al. Modulus of Subgrade Reaction for Circular Tunnels considering Bedrock and Ground Surface. KSCE J Civ Eng 27, 2593–2602 (2023). https://doi.org/10.1007/s12205-023-2029-1
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DOI: https://doi.org/10.1007/s12205-023-2029-1