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PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping, L.F. Costa Neves and R.C. Barros
On the Boundary Integral Element Method for a Solution of Shallow Tunnels using Neumann Series
Y.S. Karinski, M.Y. Antes and D.Z. Yankelevsky
National Building Research Institute, Technion-IIT, Haifa, Israel
Y.S. Karinski, M.Y. Antes, D.Z. Yankelevsky, "On the Boundary Integral Element Method for a Solution of Shallow Tunnels using Neumann Series", in B.H.V. Topping, L.F. Costa Neves, R.C. Barros, (Editors), "Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 99, 2009. doi:10.4203/ccp.91.99
Keywords: boundary element method, buried structures, half plane, openings, stress concentration, Shanks' transform, Neumann's series.
This paper presents an approach which allows the solution of elastic problems concerning a half plane with cavities using the boundary integral equation method with a Neumann's series. To evaluate the series terms at singular points, the regular representations of singular integrals for external problems were proven and the regular recurrent relationships for the series terms, which can be calculated by any known quadrature rule, are obtained. The modified Shanks' transform was incorporated to accelerate the series convergence.
The proposed procedure was tested by comparison with known theoretical solutions and the method convergence was studied for various burial depths of the cavity. To demonstrate the capability of the approach developed, a horseshoe shape opening with sharp corners was investigated and the location and magnitude of the maximum hoop stress was calculated. The dependence of the maximum hoop stress location on the parameters of the surface loading (degree of asymmetry, size of loaded area) and of the opening (the opening height) was studied. It was found that the absolute magnitude of the maximum hoop stress (for all possible surface loading locations) is developed at the roof points when the opening height/width ratio is relatively large or when the pressure loading area is relatively narrow (compared to the roof arch radius). Contrarily, when the opening height/width ratio is relatively small or when the surface pressure is applied to a relatively wide area, the absolute magnitude of the maximum hoop stress is developed at the bottom sharp corner points.
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