Geotechnika - Fakulta stavební - Vysoké učení technické v Brně

12 th International Scientific Conference, April 20-22, 2009 Brno, Czech Republic 77NUMERICAL MODELLING OF SEGMENTAL LININGUSING FEMJan PruškaOne of the main aspects of a tunnel design applies to the control the behaviour of thelining and the stress in the vicinity rock, which can involve the ageing of undergroundstructure. Several approaches have been presented by different authors in the scientificliterature with a purpose toward estimating maximum tunnel durability and thesurrounding mass extension affected by deformation phenomena. The behaviour of theunderground structures can be estimated by using empirical or semiempirical methodsand analytical methods or numerical methods. The Zurabov – Bugaeva analytical methodis one of the general used for simple obtaining the internal forces in the lining. In the caseof the numerical modelling using FEM we have to appropriately describe the behaviour ofthe segments in the tunnel lining. Thus the main focus is concern on the acting range ofthe subgrade reaction in the contact between lining and the surrounding rock mass, theeffects of joints between the segmental linings, lining parameters and the earth pressurecoefficient at rest. At the end the results of the segmental lining modeling is shown.Principles of tunnel segment lining analysisThe Zurabov - Bugaeva analytical methodWhen we compute the member forces in the lining using Zurabov Bugaeva method [1], wemust determine the acting range, the magnitude and the direction of the subgrade reaction. Thesubgrade reaction is divided into the reaction independent of the displacement of ground such andthe reaction dependent on the displacement of ground. It is assumed that the latter subgrade reactionis proportional to the displacement of ground and its factor of proportionality is defined as thecoefficient of subgrade reaction. The value of this factor depends on the ground stiffness and theradius of lining. The bedded rigid frame model evaluates the subgrade reaction as the spring force.FEM analysisIn the following part we described the factors that would induce stresses in the lining andcausing the failure of segmental tunnel lining in the respect of FEM modelling.One of the main influencing factors affecting the stresses induced in the lining is the effect of jointsbetween the segmental linings. Muir Wood [2] proposed that for a segmental tunnel ring with anumber of equal segments n, the effective moment of inertia Ie can be expressed as:2⎛4⎞Ie= Ij+ ⎜ ⎟ I Ie≤ I, n〉4⎝n⎠( 1 )Where: Ie is the effective value of I,Ij is the effective value of I at the joint,I is the moment of inertia of the lining,n is the number of segments,Ij