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将混凝土衬砌材料视为具有分数导数本构的粘弹性体,在频率域研究了深埋圆形隧洞粘弹性土的稳态动力响应。利用衬砌的内边界条件和混凝土衬砌与土体界面处的连续性条件,得到了粘弹性土体和衬砌稳态振动的应力和位移解析解。进行了隧洞衬砌厚度、土体阻尼比、本构阶数、材料参数比等对土体的位移和应力幅值影响的算例分析,结果表明:材料参数比对系统动力特性有较大影响,随着材料参数比的增加,位移和应力幅值减小;随着土体的阻尼比、衬砌厚度的增加,位移和应力幅值减小;当材料参数比Tσ/Tε=3时,随着分数导数阶数增大,响应幅值减小。
Considering the concrete lining material as a viscoelastic body with fractional derivative constitutive, the steady-state dynamic response of deep-buried circular tunnel viscoelastic soil is studied in the frequency domain. By using the inner boundary condition of lining and the continuity condition of concrete lining and soil, the analytical solution of stress and displacement of viscoelastic soil and lining is obtained. The influence of tunnel lining thickness, soil damping ratio, constitutive order and material parameter ratio on the displacement and stress amplitude of soil mass is analyzed. The results show that the material parameter ratio has a great influence on the dynamic characteristics of the soil, With the increase of material parameter ratio, the displacement and stress amplitude decrease. With the damping ratio of soil and lining thickness increasing, the displacement and stress amplitude decrease. When the material parameter ratio Tσ / Tε = 3, Fractional derivative order increases, the response amplitude decreases.