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Title: Earth vibration effects and abatement for military facilities. Report 3, Analysis method for footing vibrations through layered media
Authors: Waas, Günter.
Keywords: Foundations
Numerical analysis
Electronic data processing
Ground motion
Military facilities
Wave propagation
Publisher: Soils and Pavements Laboratory (U.S.)
Series/Report no.: Technical Report;S-71-14, Report 3
Abstract: Abstract: A numerical method is presented for the analysis of steady-state wave propagation problems in linearly elastic or viscoelastic media of infinite extent. Plane and axisymmetric geometries are considered which consist of a finite irregular region joined to semi-infinite layered regions. By this method, torsional and vertical vibrations of circular footings on, or embedded in, homogeneous and inhomogeneous soil layers over rock are studied. The irregular region is discretized by compatible finite elements, while the semi-infinite layered regions are discretized by subdividing the layers into thin sublayers and by assuming that within each sublayer the displacements vary linearly in the direction normal to the layers. In the direction parallel to the layers, the displacements are expanded into a finite number of plane or axisymmetric propagating and decaying wave modes which are determined by the solution of algebraic eigenvalue problems. Dynamic stiffness matrices are developed which uniquely relate nodal forces to simultaneous nodal displacements at the boundary between the irregular and the layered regions and thus represent the dynamic response of the semi-infinite layered regions. The dynamic stiffness of the combined regions is computed by the direct stiffness method. The equations of motion are derived from the principle of virtual work which is formulated to facilitate the use of complex variables in the analysis of the harmonic motion . Solutions obtained by this numerical method show good agreement with known analytical solutions . The response of circular footings, which are supported by soil layers over rock and are excited to vibrate in the torsional and vertical mode, are investigated; the effects of the thickness of the supporting layer, embedment of the footing and increasing shear modulus with depth are studied. The screening effect of trenches on horizontally polarized shear waves is explored by varying the trench depth and the frequency of the wave motion.
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