Presenting a simple method to estimate ground deformations in building-tunnel interaction

Constructing underground tunnels in urban areas brings surface buildings close to excavations, leading to mutual deformation effects between tunnels and structures. Analyzing this interaction is challenging due to soil nonlinearity and complex building characteristics. In this study, a simplified method based on two- and three-dimensional finite element numerical analyses is presented to estimate the values of surface deformations of ground, tunnels, and buildings. Also, the maximum cross-section of the Kermanshah urban train tunnel has been used to perform numerical modeling. Logical and facilitating simplifications in the definition of tunnel-building interaction are presented to solve the problem more quickly. The obtained deformation values ​​have been compared and verified with the actual values ​​measured in other available valid references. A good agreement is observed between the results of field measurements and the numerical findings of this study. Accordingly, vertical displacement modeling yields a difference between 1.45% and 6.67% when comparing valid field results and the 2D finite element numerical model. In addition, the difference between the overall displacement results of the NATM staged tunneling model in the 3D model of the reference article and the 3D model of this study is a negligible 7.14%. Also, a simple and short-exponential mathematical equation with high accuracy (coefficient of determination greater than 0.90) is presented to estimate the amounts of deformations, efforts, and internal forces of the tunnel lining system with increasing surface construction overhead. A simple exponential mathematical relationship with an increasing upward trend with high fitting accuracy has been obtained between the changes in horizontal displacement responses, settlement, shear stress, shear strain, internal efforts of the reinforced concrete lining of the tunnel (bending moment, shear force, and axial force), and the surface structure overhead. On the other hand, the amounts of horizontal displacements of the soil mass above the tunnel crown is about 25% of the vertical displacements (settlements).