黏弹性分数导数型饱和土中球形空腔的动力响应

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。

Dynamic response of a spherical cavity in viscoelastic fractional derivative type saturated soil

Based on the Biot's consolidation theory, the dynamic response of a spherical cavity in viscoelastic fractional derivative type saturated soil is investigated in the frequency domain. The stress and strain constitutive relation of the soil skeleton is described by the fractional derivative type viscoelastic model. By utilizing a stress coefficient depending on the porosity of soil, the values of the inner water pressure in lining and in pore water are determined, respectively. Based on the continuity conditions at the interface between the soil and the lining, the steady-state dynamic response of the spherical cavity in fractional derivative type viscoelastic saturated soil subjected to the inner water pressure is obtained. The influences of physical parameters on the response amplitudes are studied, and it is revealed that their influences on the system response are remarkable by the viscosity of soil, the characteristics of materials and the relative permeabilities of the pore flexible lining and saturated soil.