Similarity Solution for the Synchronous Grouting of Shield Tunnel Under the Vertical Non-Axisymmetric Displacement Boundary Condition (Advances in Applied Mathematics and Mechanics, 2018)
Similarity solution is investigated for the synchronous grouting of shieldtunnel under the vertical non-axisymmetric displacement boundary condition in thepaper. The synchronous grouting process of shield tunnel was simplified as the cylindricalexpansion problem, which was based on the mechanism between the slurry andstratum of the synchronous grouting. The stress harmonic function on the horizontaland vertical ground surfaces is improved. Based on the virtual image technique,stress function solutions and Boussinesq's solution, elastic solution under the verticalnon-axisymmetric displacement boundary condition on the vertical surface was proposedfor synchronous grouting problems of shield tunnel. In addition, the maximumgrouting pressure was also obtained to control the vertical displacement of horizontalground surface. The validity of the proposed approach was proved by the numericalmethod. It can be known from the parameter analysis that larger vertical displacementof the horizontal ground surface was induced by smaller tunnel depth, smaller tunnelexcavation radius, shorter limb distance, larger expansion pressure and smaller elasticmodulus of soils.