When excavating a tunnel, the stresses are distributed asymmetrically along the tunnel cross-section. Other factors, particularly slope friction force and excavation speed, can also contribute to the deformation and displacement of a tunnel. Despite this, several authors have used the complex potential method to predict the ground deformation surrounding the tunnel. However, their applicability to the ground response caused by the asymmetric stress distribution around the tunnel wall is analysed in this context. This paper, therefore, proposes an approximate solution on the slope to predict the tunnel cross-section deformation. The solution is based on the complex potential method to predict analytically and numerically the ground deformation around the tunnel. However, two variables called the “complex potential functions” for the Laurent series expansion are used for the stress redistribution to the tunnel boundary conditions. Data from the Qijiazhuang tunnel case are used to justify the proposed analytical solutions. This solution is an essential guide for analyzing deformations in complex geological conditions and structures, such as steeper slopes.

This paper proposes analytical solutions to the soil deformation around a cylindrical cavity under drained conditions. Analytical procedures are used to predict the degree of interaction between cavities and ground surface loads based on mathematical theorems. The stresses applied at the boundary condition induce the ground motions around the cylindrical cavity wall. Additionally, the Airy stresses are obtained through mathematical derivatives and integrations by combining the Fourier analysis test with the Navier equations. Next, we established a schematic representation of the horizontal and vertical displacement related to the corrective shear model to obtain insight into the intensity and directions of ground stresses. The resulting transformations include displacement, shear, and deviatoric stresses applied to the cylindrical cavity wall. These data can be used as input parameters for numerical simulations to alternatively solve the groundmass redistribution problems and calibrate the horizontal stress of drained soil conditions.