The tunnels are one of the most important constructions that shorten the time and facilitate the transition between difficult places such as highlands and mountains. It is one of the reasons countries grow economically. The tunnels must be safe in all situations. The engineer must take into consideration the quality of the soil and rock in the place of excavation, the appropriate method of excavation, the location of the tunnel, and the materials used, as well as the design of the tunnel without forgetting the appropriate shape of the tunnel. In this paper, we simulated the model with various shapes ("seven shapes") by using the finite element method Optum G2 software. The stability research for the various tunnel shapes was carried out by examining soil settlements, horizontal, vertical displacement, shear, normal forces, and a bending moment of the lining concrete of these shapes.

The presence of barriers in point-plane oil gaps has an important role on the insulating oil dielectric strength. This latter closely related to the nature (material), the thickness and the diameter of the barrier, its relative position, the distance between electrodes and theirs interactions. The present work is devoted to estimate the dielectric strength of the transformer oil, the Borak 22 under 50 Hz ACvoltage, in presence of Bakelite and Pressboard barriers of 2 and 4 mm thicknesses. To achieve this goal, proposal mathematical models have been built via Central Composite Face method (CCF) which is a robust tool introduced by FISHER. It allowed us to estimate the dielectric strength through a mathematical model. For each barrier, the formulation and the verification of the established models are carried out for several inter-electrodes distance (d=4, 6, 8 10 and 12cm) and relative positions of the barrier (a/d=20, 40, 60, 80 and 100%; a being the point-barrier distance). For each configuration, the corresponding model is verified using graphical and statistical analyses. It is validated as long as the relative mean error between the estimated dielectric strength values and the experimental ones.