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基于Biot理论,在频率域内研究了黏弹性分数导数型饱和土中球形空腔的动力响应。利用分数阶导数黏弹性模型描述土骨架的应力–应变本构关系,并采用与土体孔隙率有关的应力系数合理地确定了衬砌和孔隙水分别承担的内水压力值。通过土体和衬砌接触面处的连续性边界条件,得到了内水压力作用下黏弹性分数导数型饱和土体中球形空腔的稳态动力响应。考察了物性参数对响应幅值的影响,研究表明:土体黏性和材料特性以及多孔柔性衬砌和饱和土的相对渗透性,对系统响应有较大的影响。
Based on Biot theory, the dynamic response of spherical cavity in viscoelastic fractional derivative saturated soil is studied in the frequency domain. The fractional-derivative viscoelastic model is used to describe the stress-strain constitutive relation of soil skeleton, and the stress coefficient related to porosity of soil is used to reasonably determine the internal water pressure assumed by lining and pore water respectively. The steady state dynamic response of spherical cavity in viscoelastic fractional derivative saturated soil under internal water pressure is obtained through the continuity boundary conditions at the contact surface of soil and lining. The influence of physical parameters on the response amplitude was investigated. The results show that the relative viscosity of soil and the permeability of porous flexible lining and saturated soil have a great influence on the system response.