An empirical model for characterizing 3D deformation at the face of shield tunnel in soft clay

•An improved numerical model to study the gap parameter were adopted.•3D deformation at the tunnel face of tunnelling in soft clay were studied.•An empirical model to depict the 3D deformation at the tunnel face were established.•This empirical model can be used further to estimate the gap parameter. Accurate estimation of potential ground movement due to tunnelling is fundamental for safety evaluation of adjacent facilities. Gap parameter is a simple but important parameter widely used for predicting ground loss of tunnelling. The existing estimation method for u*3D, a gap parameter component induced by 3D deformation at tunnel face, tends to show several aspects of limitations owing to some oversimplified assumptions. In this study, the improved numerical model is first established to study the characteristics of 3D deformation at tunnel face. Then, the impacts of 4 key parameters relevant to tunnelling on the horizontal intrusive displacement at tunnel face are discussed extensively. Finally, an empirical model for characterizing the 3D deformation at tunnel face is developed and verified by comparing to the numerical modelling results. It is shown that the proposed empirical model is able to predict the 3D deformation at tunnel face reasonably. This empirical model can be further utilized to estimate the magnitude of u*3D.