Investigation of static and dynamic behaviors of a layered semi-infinite medium with twin tunnel by using finite and infinite elements

Tunnels in metropolitan cities; used to meet many different needs such as traffic, mining, military facilities, and the passage of underground cables. The use of shallow tunnels, especially in metropolitan cities, has been increasing in line with the need in recent years. The interaction of tunnels in medium with different parameters with the structures on the surface, the medium and the tunnels with each other has become an important issue. In this study, linear and nonlinear static and dynamic analyzes of the layered semi-infinite medium containing twin tunnels performed. Different stiffnesses of the semi-infinite layered medium, the situation of voids, and the situation of twin tunnels at different locations in the layered medium investigated. In the cavity and tunnel sections, geometrically square-section tunnels and cavities considered. A linear elastic material model were used in linear analyses, and a bilinear stress-strain material model were used in non-linear analyses. In static analyses, vertical displacement and normal stress behaviors in different models examined. In dynamic analyses, displacement and acceleration results in a certain time domain in semi-infinite medium under the influence of harmonic and impact loads examined. Newmark Beta method used to examine the behavior under the influence of dynamic load. Finite element method used in numerical analysis. In static and dynamic analyzes at certain boundary conditions accepted in the finite region, serious errors occur due to the reflection of load effects depending on the boundary conditions. Considering this situation, the finite-infinite element model, which accepts the semi-infinite medium as a whole, was used. The finite-infinite element model is modeled with finite elements in the region close to the load effect, and the infinite medium away from the load effect is modeled with infinite elements depending on its direction. In order to be compatible with the structures inside and to shorten the calculation time, a 16-node finite element used. In the infinite environment, an infinite element with 8 nodes that goes to infinity in the direction of the infinite region compatible with the model is used. Infinite elements with 4 nodes, compatible with the finite-infinite model, used at the corner points of the models. Infinite element shape functions produced to be compatible with 16-node finite elements. The equations obtained in the finite-infinite element model solved by the 5-node Gauss Legendre integration method. In the nonlinear static analysis solution, the incremental load method applied. In the first stage of the solution of nonlinear dynamic analysis, the dynamic loads affecting the system divided by a certain finite number and applied incrementally depending on the time and load function. The time interval corresponding to each load step was determined from the load function and the solution was made with the Newmark Beta method. A comparison study conducted to test the accuracy of the static and dynamic results and the results verified. Boussinesq theory used to verify the static results. For dynamic results, an medium modeled in the PLAXIS package program and dynamic analysis performed and the results compared. To determine the number of finite elements, a convergence study carried out in static analysis. Modeling done using the MATLAB program, and the resulting equations and algorithms coded. Numerical results and graphics obtained using the MATLAB program. The coded program automated to a certain extent. As the numerical results examined, in order to obtain realistic results and reduce the computational cost in semi-infinite medium problems involving twin tunnels; the finite-infinite element model is designed together, and the non-linear form of the material model should be taken into account. The region close to the load effect should be modeled with finite elements, and the remote region should be modeled with infinite elements. An important result for practical applications is that all boundary conditions of such problems can be taken into account with the infinite element model used.