Finite element analysis of dynamic structure-medium interaction with some reference to underground nuclear reactor containments

A finite element solution is developed for the problem of time-history response of reinforced underground cavity subjected to dynamic disturbances of the underground environment. The cavity can be of any shape, reinforced by either rock bolts or any elastic liner, with bending stiffness taken into consideration. Available methods that can solve the cavity problem are examined and an available computer programme (plane stress) modified. Introduction of a new reinforcing plate element necessitated development of two new subroutines and the extension of a third one along with certain modifications in the other subroutines and the main programme for matching requirements. The modifications enable the determination of displacements and the internal forces - time histories of the liner. -- A quantitative study of the following parameters that affect the response of the cavity reinforcement and the surrounding medium is carried out: 1) cavity reinforcement, 2) cavity shape, 3) isolation of the entire structure from the surrounding medium by a soft, energy absorbing material and 4) properties of the filling material in the cut-and-cover structural type. The modified computer programme has applications to problems outside the field of two-dimensional rock-structure interaction such as the dynamic analysis of beams, plane frames and arches. -- A finite element model is developed to simulate the dynamic analysis of infinite space. The results of the study indicate that reinforcing the cavity by a steel liner decreases the stresses in the medium by about 10% while the use of a rock bolting pattern with about 80% of the amount of steel required in a reinforcing liner decreases the stresses around the cavity by 25% and more. The horseshoe shape proves to be the best among the various shapes considered decreasing the stresses by 10-15%. Large reductions (of the order of 80%) in shell (liner) membrane forces and bending moments are reached by isolating the entire structure from the surrounding medium by a soft, energy absorbing material, which agree with the results from another investigation. It is also pointed out that a proper selection of the properties of the filling material in the cut-and-cover structure can reduce the internal forces in the structure and the stresses in the adjacent medium. It is shown that a significant reduction cannot be achieved by a single property variation but only through a proper combination of different properties (Figs. 33 to 36). The results obtained from the new model indicate the need for further modelling work in the solution of earthquake interaction problems for underground cavities