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| Analytical solution for seismic response of large diameter, double-layer concrete-lined shafts in unsaturated soil under vertically-incident P-waves |
| YANG Jiale1，DI Honggui1*，YAO Yanming2，ZHOU Shunhua1，ZHANG Xiaohui1，HE Chao1 |
(1. Shanghai Key Laboratory of Rail Infrastructure Durability and System Safety, Tongji University, Shanghai 201804, China;
2. Ningbo Rail Transit Group Co., Ltd., Ningbo, Zhejiang 315101, China) |
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Abstract Based on the theory of three-dimensional continuum mechanics, an analytical model was developed to investigate the seismic response of large-diameter, double-layer concrete-lined shafts in unsaturated soil subjected to vertically incident P-waves. The three-dimensional dynamic governing equations for unsaturated soils were established, taking into account capillary pressure and a saturation-dependent dynamic shear modulus. The double-layer shaft lining was idealized as two parallel Rayleigh-Love rods to account for their transverse inertial effects.
Initially, the free-field response of the unsaturated soil was determined using one-dimensional wave propagation theory. Subsequently, the wave equations of the soil were solved through the potential function method, operator decomposition, and the separation of variables. A closed-form solution for the seismic response of the shaft was derived by applying the boundary conditions of the coupled soil-shaft system. The model proposed in this study was validated through comparison with existing results and followed by a parametric sensitivity analysis to evaluate the influence of soil saturation, shaft geometry, and material properties on the seismic response. The results indicated that the seismic response of large-diameter, double-layered shafts is significantly influenced by the excitation frequency: the low-frequency behavior is governed by the static characteristics of the shaft, while the high-frequency response is dominated by the soil-structure dynamic interaction. As soil saturation increases, both the natural frequency of the system and the kinematic amplification factor at the shaft head decrease. Additionally, the transverse inertial effect of the double-layer lining has a negligible impact within the primary frequency range of vertical seismic loading. The proposed analytical framework provides a theoretical basis for the seismic design and safety assessment of shafts in unsaturated ground.
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2026, Vol. 45 
