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 引用本文: 郭慧吉, 狄宏规, 周顺华, 何超, 张小会. 非饱和土-隧道系统动力响应计算的波函数法[J]. 力学学报, 2020, 52(2): 591-602.
Guo Huiji, Di Honggui, Zhou Shunhua, He Chao, Zhang Xiaohui. WAVE FUNCTIONS METHOD FOR CALCULATING THE DYNAMIC RESPONSE OF A TUNNEL IN UNSATURATED SOIL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(2): 591-602.
 Citation: Guo Huiji, Di Honggui, Zhou Shunhua, He Chao, Zhang Xiaohui. WAVE FUNCTIONS METHOD FOR CALCULATING THE DYNAMIC RESPONSE OF A TUNNEL IN UNSATURATED SOIL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(2): 591-602.

## WAVE FUNCTIONS METHOD FOR CALCULATING THE DYNAMIC RESPONSE OF A TUNNEL IN UNSATURATED SOIL

• 摘要: 针对非饱和地基土中埋置隧道的三维动力响应计算问题, 提出了波函数法.采用无限长的Flügge薄壁圆柱壳模拟圆形隧道衬砌,采用流、固、气组成的三相介质模拟非饱和地基土体.分别采用分离变量法以及Helmholtz矢量分解定理求解薄壁圆柱壳的振动控制方程与非饱和土的波动方程.根据隧-土交界面与地表面处的应力、位移以及孔隙流体压力等边界条件,利用平面波与柱面波的转换性质,实现了隧道内作用单位简谐载荷时隧道衬砌与土体系统动力响应的耦合求解.通过与既有单相弹性介质2.5维有限元-边界元法、两相饱和多孔介质2.5维有限元-边界元法以及三相非饱和介质Pip in Pip半解析法的计算结果进行对比, 验证了本文计算方法的可靠性. 最后,基于该方法, 通过算例分析了不同饱和度下非饱和土-隧道系统的动力响应特征.结果表明, 饱和度对土体动位移与超孔隙水压力的幅值响应有较大影响.该方法的非饱和地基土参数退化后,也可用来计算和分析饱和地基土或单相弹性地基土与隧道系统的动力响应.

Abstract: This paper presents a wave functions method to calculate the three dimensional dynamic interaction between a circular tunnel and the surrounding unsaturated foundation soil. The tunnel lining is conceptualized as an infinite Flügge cylindrical shell, and the unsaturated foundation soil is conceptualized as a three-phase medium consisting of fluid, solid and gas. The motion equations of infinite Flügge cylindrical shell are solved by the separation of variable method, and the Helmholtz decomposition theorem is used to solve the unsaturated soil governing equations. Based on the boundary conditions of displacement, stress and pore fluid pressure at the unsaturated soil-tunnel interface and the ground surface, the dynamic interaction between the unsaturated soil and circular tunnel is solved when the tunnel invert subjected to a unit harmonic load. The transformation properties of plane wave functions and cylindrical wave functions are used to apply the boundary conditions expressed in both the rectangular and cylindrical coordinate systems before the coupling. The proposed method is verified by comparing with the results obtained by the existing 2.5 dimensional coupled FE-BE method for single phase elastic medium, 2.5 dimensional coupled FE-BE method for two phase saturated porous medium and Pip in Pip semi analytical method for three-phase unsaturated medium. Finally, by using the proposed method, the dynamic response of the unsaturated soil-tunnel system under different soil saturations is analyzed by a case study. The results show that saturation has a great effect on the dynamic response amplitude of soil displacement and excess pore water pressure. Because the three-phase medium simulating unsaturated soil can be reduced to two-phase medium or single-phase medium, this method can also be used to calculate and analyze the dynamic response of a circular tunnel buried in two-phase saturated soil or in single-phase elastic soil after the degeneration of the calculation parameters of unsaturated soil.

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