Stress-displacement solution for a lined vertical borehole due to non-axisymmetric in situ stresses

By using the semi-inverse method, an elastic plane stress solution of a lined vertical borehole in an isotropic ground due to non-axisymmetric in situ loads is presented. As two extreme cases, pure bond and pure slip boundary conditions, along the liner/ground interfaces have been implemented. The effect of elastic modulus of liner and ground and thickness of liner upon the stresses and displacements are analyzed. The result indicates that soft liner may alleviate the normal stress and shear stress acting on the liner outer surface. The maximum tangential compressive stresses and tensile stresses in liner for two extreme boundary cases occur on the inner and outer boundaries of liner. The shear stress reaches the maximum value at θ=45° and the harder the liner is, the greater the maximum value is.

► A vertical shaft remotely loaded by in situ stresses belongs to a space problem.
► Space problems can be simplified as the corresponding plane stress problems.
► The load acting on the outer surface of liner can be calculated simultaneously.
► Solution obtained by this paper is closer to the actual situation.