Ring distribution model of filling pressure for shield tunnels under synchronous grouting

To define the magnitude and distribution of filling pressure of synchronous grouting, the theory of fluid mechanics is employed to describe the filling process. Considering that the speed of shield driving is very slow and that the required time of the slurry flowing to the furthest position along the ring is very short, and supposing that the slurry fills the shield tail interspace only along the ring, a three-dimensional circular thin cake is formed. A ring distribution of filling pressure for shield tunnels under synchronous grouting is derived under the Bingham fluid and the Newtonian fluid conditions. The application scope of the model and the calculation method of its main parameters are studied. The validity of the model is certified by use of the monitoring results obtained from certain practical engineering cases, and the distribution laws of filling pressure and the relevant parameters are also analyzed. The results show that the calculated values by the proposed model agree well with the measured ones, that the variation of filling pressure along the ring is caused by the slurry weight and the shear stress, and that the calculated values under the Bingham fluid are slightly less than those under the Newtonian fluid.