Explicit Peck formula applied to ground displacement based on an elastic analytical solution for a shallow tunnel

Using the complex variable method, an elastic analytical solution of the ground displacement caused by a shallow circular tunneling is derived. Non-symmetric deformation relative to the horizontal center line of the tunnel cross-section is used as a boundary condition. A comparison between the proposed analytical method and the Finite Element Method is carried out to validate the rationality of the obtained analytical solution. Two parameters in the Peck formula, namely the maximum settlement of the ground surface center and the width coefficient of settlement curve, are fitted and determined. We propose a modified Peck formula by considering three input parameters, namely the tunnel depth, tunnel radius, and the tunnel gap. The influence of these three parameters on the modified Peck formula is analyzed. The applicability of the modified Peck formula is further investigated by reference to six engineering projects. The ground surface displacement obtained by the explicit Peck formula is in good agreement with the field data, and the maximum error is only 1.3 cm. The proposed formula can quickly and reasonably predict the ground surface settlement caused by tunnelling.