**5. Numerical methods**

In tunnel design, empirical solutions and analytical solutions do not always give exact results. Numerical analysis and solutions are required for complex geological structures and complex underground structures. The Finite Element Method, Finite Difference Method and Discrete Element Methods are used as common numerical analysis methods. Numerical analysis methods are used both in 2D and 3D. Numerical programs have been increasingly used in tunnel design in recent years. In numerical programs, in-situ conditions, geological units and boundary conditions can be reflected exactly. In addition, while creating the models, the tunnel geometry, excavation stages and support details can be entered into the model exactly.

In numerical methods, the stresses and strains occurring in the ground can be calculated and the cross-sectional effects on the support systems can also be

determined. Thus, much more accurate results can be obtained compared to empirical and analytical solutions for design.
