Analytical Method for Evaluating the Ground Surface Settlement Caused by Tail Void Grouting Pressure in Shield Tunnel Construction

The tail void grouting is a key step in shield tunnel construction and has an important influence on the loading on the surrounding soil and on the resulting settlement. In order to estimate the ground surface settlement caused by tail void grouting pressure in tunnel construction, the loading on the surrounding soil is simplified as an expansion problem of the cylindrical cavity in semi-infinite elastic space. A simple analytical formula is deduced by using the virtual image technique and Fourier transform solutions. The effectiveness of the proposed method is verified by case studies. The effects of elastic modulus, tail void grouting pressure, tunnel radius, and tunnel depth on the ground surface heave are conducted. The results indicate that the computed results are in accordance with Ye’s solution and it is more rational to consider the ground surface heave induced by tail void grouting pressure in the prediction of ground settlement due to shield excavation. Moreover, the ground surface heave owing to tail void grouting pressure resembled a Gaussian distributed curve. Thus, no matter the ground surface subsidence or ground surface heave can be predicted by means of adding the presented empirical formula to the Peck formula which cannot predict the ground surface heave. The ground surface heave decreases with an increase in elastic modulus. On the contrary, as the tail void grouting pressure and tunnel radius increase, the ground surface heave increases, respectively. The ground surface heave first steadily increases and then declines gradually with the tunnel depth increase.