Similarity Solution for the Synchronous Grouting of Shield Tunnel Under the Vertical Non-Axisymmetric Displacement Boundary Condition

Abstract.Similarity solution is investigated for the synchronous grouting of shield tunnel under the vertical non-axisymmetric displacement boundary condition in the paper.The synchronous grouting process of shield tunnel was simplified as the cylindrical expansion problem,which was based on the mechanism between the slurry and stratum of the synchronous grouting.The stress harmonic function on the horizontal and vertical ground surfaces is improved.Based on the virtual image technique,stress function solutions and Boussinesq’s solution,elastic solution under the vertical non-axisymmetric displacement boundary condition on the vertical surface was proposed for synchronous grouting problems of shield tunnel.In addition,the maximum grouting pressure was also obtained to control the vertical displacement of horizontal ground surface.The validity of the proposed approach was proved by the numerical method.It can be known fromthe parameter analysis that larger vertical displacement of the horizontal ground surface was induced by smaller tunnel depth,smaller tunnel excavation radius,shorter limb distance,larger expansion pressure and smaller elastic modulus of soils.

Spatial distribution model of the filling and diffusion pressure of synchronous grouting in a quasi-rectangular shield and its experimental verification

Considering that the particular geometric shape of a quasi-rectangular shield,the grout flowing law and its motion process are more complicated than those of a conventional circular shield.To interpret the grouting mechanical ehaviour in the special-shape shield tail void,the filling and diffusion mechanism of synchronous grouting was analysed.The grout flowing is separated into two independent motion processes,which contains a circumferential filling and a longitudinal diffusion.The theoretical model of the grout pressure spatial distribution was derived based on the principle of fluid mechanics.Then,the pressure distributions in the two directions were obtained using a case study and compared with the field measured data to verify the validation of the model.Although the overall spatial pattern of grout pressure distribution on the tunnel profile show a change trend dominated by the self-weight effect mostly,its local fluctuation characteristics is very abnormal relative to that of a circular shield tunnel.Moreover,the important factors in the model were analysed,including the grout material parameters,the grouting construction parameters,and some geometry parameters.The results show that the pressure loss along this way is positively correlated with the grout flow velocity and is sensitive to the shear yield stress of the grout.The pressure loss along the circumferential direction is the most sensitive to the thickness of the ring cake,and the value range suitable for the model should be 0.02-0.03 m.The pressure loss along the longitudinal diffusion direction is the most sensitive to the size of the tail void.The research results can provide a theoretical basis for the control of special-shape shield construction.