The Analytical Solution of Stress and Displacement for Multi-layer Cylinder Under Radial Seepage

The buried depth of vertical shaft is large, most of them pass through water rich rock stratum and bear high head internal water pressure. The influence of seepage field on its surrounding stress field and displacement field can’t be ignored. Based on the plane stress model, the mechanical model of multi-layer cylinder under steady seepage is proposed in this paper. Firstly, the seepage field of single-layer cylinder and multi-layer cylinder is resolved. Secondly, based on the plane stress model, the general solution and definite solution formula of stress and displacement of single layer cylinder under seepage force are derived. Finally, analytical solutions of stress and displacement of the cylinder under penetrability, internal pressure and external pressure are derived. A general solution for the interlayer radial forces is provided. An example is analyzed with considering fluid flow field. The research shows that the elastic modulus ratio is the most important factor affecting the interlayer force transfer, and the Poisson's ratio has little effect on the change of stress.