Predicting the grouting effect on leakage-induced tunnels and ground response in saturated soils

•A new set of analytical solutions for predicting the effect of tunnel leakage is proposed.•A simplified model is proposed to quantitatively describe the effect of grouting on tunnel leakage.•The tunnel leakage state can be easily evaluated using the simplified model.•The effect of grouting on tunnel leakage is affected by tunnel lining permeability.•The leakage induces significant settlements rather than tunnel convergence and internal forces. This paper suggests a new set of analytical solutions for predicting the effect of grouting on ground and shield tunnel behaviour as a consequence of steady water inflow into a tunnel in saturated clay. These solutions allow the effects of the tunnel lining and grouting material to be considered on the basis of their relative permeability to the surrounding soil. Moreover, the equivalent permeability of the tunnel lining can be derived based on the water inflow rate, which is commonly assumed to be proportional to the soil permeability in a typical analysis. A comparison of the results of analytical and numerical simulations indicates that the solutions are sufficiently accurate for tunnel applications. The effect of grouting material on the tunnel-leakage-induced seepage field, ground and tunnel settlements, internal forces and tunnel convergence of the shield tunnel are examined with the verified solutions. Based on the analytical results, the effect of grouting material on the tunnel leakage appears to depend on the permeability of the tunnel lining. Thus, a dimensionless parameter RPslg integrating the permeability and geometry of the tunnel lining and grouting material is proposed to quantitatively describe the effect of the grouting material on tunnel leakage. Using RPslg, the effect of the grouting material on tunnel leakage can be easily derived. Indeed, the analytical results show that tunnel leakage produces significant ground and tunnel settlement. The grouting can clearly reduce the effect of tunnel leakage on tunnel and ground settlement when the relative permeability of the grouting material and soil kg/ks is less than 0.01. Moreover, the increase in the tunnel-leakage-induced bending moment and the decrease in hoop thrust are generally small but this may increase the permeability of the tunnel joints. The leakage-induced tunnel convergence is small and is therefore unlikely to degrade the serviceability or safety of a tunnel.