Abstract This paper investigates the fractional non-axisymmetric consolidation of stratified cross-anisotropic visco-poroelastic media. Firstly, based on the Laplace–Hankel transform, the ordinary differential equations of cross-anisotropic poroelastic media are derived, which are extended to those of fractional visco-poroelastic media by introducing the fractional Merchant model and the elastic-viscoelastic correspondence principle. Then, the extended equations are solved by the extended precise integration method (PIM), and the proposed theory is compared with the results reported in the references. Finally, selected numerical examples are performed to investigate the effects of the order of fractional derivative, viscoelasticity, cross-anisotropy and stratification on the non-axisymmetric consolidation.

中文翻译：

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分层交叉各向异性粘孔弹性介质的部分非轴对称固结

摘要 本文研究了分层交叉各向异性粘孔弹性介质的部分非轴对称固结。首先，基于Laplace-Hankel变换，推导了交叉各向异性多孔弹性介质的常微分方程，通过引入分数Merchant模型和弹粘弹性对应原理，将其推广到分数粘多孔弹性介质的常微分方程。然后，通过扩展精确积分方法（PIM）求解扩展方程，并将所提出的理论与参考文献中报告的结果进行比较。最后，通过选定的数值算例，研究了分数阶导数、粘弹性、交叉各向异性和分层对非轴对称固结的影响。