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将无限长圆形隧道洞视为平面应变问题,借助分数导数理论、粘弹性理论和土动力学建立了分数导数粘弹性土体的极坐标运动方程,利用贝塞尔方程的性质和问题的边界条件求解了粘弹性土体运动方程的解,得到了简谐荷载作用下分数导数粘弹性土体中圆形隧道洞的径向应力和位移的表达式。通过数值算例研究了分数导数的阶数和模型参数对圆形隧道洞应力和位移的影响。
Considering the infinite circular tunnel as a problem of plane strain, the polar coordinate equation of fractional derivative viscoelastic soil was established by means of fractional derivative theory, viscoelastic theory and soil dynamics. By using the properties of Bessel equation and the boundary of the problem The solution of viscoelastic soil equation of motion is obtained. The expression of radial stress and displacement of circular tunnel in fractional derivative viscoelastic soil under simple harmonic loading is obtained. Numerical examples are used to study the influence of order of fractional derivative and model parameters on the stress and displacement of circular tunnel.