tailieunhanh - Earthquake resistant design of underground structures and pipes

Underground Structures and Pipes can be analysed as slender structures completely embedded in the soil. For the dynamical analysis soil and structure can be investigated by decoupled structural models. The horizontal layer system of the soil is modeled as a shear beam while for the structure a flexural beam is used Both models will be finally coupled by elastic foundation. | T~p chi Ca h9c Journal of Mechanics, NCNST of Vietnam T. XVII, 1995, No 3 (5 - 11) EARTHQUAKE RESISTANT DESIGN OF UNDERGROUND STRUCTURES AND PIPES DIETER KRAUS University of the German Armed Forces Munich Werner Heisenberg Weg 99 8014 Neubiberg /Germany SUMMARY. Underground Structures and Pipes can be analysed as slender structures completely embedded in the soil. For the dynamical analysis soil and structure can be investigated by decoupled structural models. The horizontal layer system of the soil is modeled as a shear beam while for the structure a flexural beam is used Both models will be finally coupled by elastic foundation. 1. INTRODUCTION For an earthquake resistant design usually the following verifications have to be carried out: (1) Stress and strain in longitudinal direction of , due to the earthquake waves which are travelling through the soil The structure has to follow the displacements of the soil, this yields to bending moments, shear forces and axial forces in longitudinal direction. In cas~ of joints, the movements of the joints has to be determined to design the joint - construction. (2) Stress and strain in transverse direction of the s~ructure, due to the reduced internal friction of the soil. Depending on the vibrations the internal friction of the soil can significant decrease up to zero. This effect is called [1} "soilliquifaction, Since soil and structure move largely together, for the calculation in transverse direction the assumptions of the "earth pressure at rest" considering the actual internal friction can be used. 2. NOTATIONS x, 1Jr-Z :coordinates u, tJ : displace~ents strains e, 1: p : mass density E: modulus of elasticity of the soil G: modulus of shear of the soil p.: Poisson's ratio of the soil ell : Shear wave velocity Cp: compressional wave velocity ).; wave length n-th frequency fn : n-th circular frequency n-th mode participation factor of the n-th mode rn: D: damping ratio modal damping of the n-th .