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Underground structures often have abrupt changes in structural stiffness or ground conditions such as junctions of tunnels, tunnel portal in slopes, and niches in road tunnels. At these locations, stiffness differences may subject the structure to differential movements and generate stress concentrations. Because of adversity in these issues, they need a three dimensional analysis. This paper proposes a numerical approach to the hyperstatic reaction method (HRM) for three dimensional analysis of permanent tunnel linings. In this paper, three dimensional numerical modelling is performed by considering hyperstatic reaction concepts. Designing is done for Manjil-Rudabar freeway project, Tunnel No. 2. The numerical analyses performed for Operational Design Earthquake (ODE) and Maximum Design Earthquake (MDE) loading conditions. Then interaction diagram between axial force and bending moment used for investigating the capacity of tunnel lining. The numerical results show that although more axial forces are created in tunnel lining for ODE condition, but the points in the P-M diagrams are located in the furthest distance to the diagram border (tunnel supporting system); because of less bending moment in this condition. Therefore, the safety factor in ODE condition is more than MDE condition. This numerical processing presented that the HRM is a proper, fast, and practical method for tunnel designers.

Application of Hyperstatic Reaction Method for Designing of Tunnel Permanent Lining, Part II: 3D Numerical Modelling