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UBC Theses and Dissertations

A non-linear dynamic finite element analysis Quong, Wayne


A two-dimensional finite element method of analysis for predicting the stress and permanent displacements of earth structures to seismic loading is presented. The inelastic behavior of the soil is modelled by an incremental linear approach in which the tangent shear modulus is varied with the level of both the shear strain and the mean normal stress. The2 shear modulus strain dependency is based on hyperbolic relationships governing initial loading and unloading behavior, leading to a hysteretic type energy dissipation. The tangent bulk modulus is varied with the level of the mean normal stress only, and hysteretic effects are not considered. The incremental linear equations of motion of the structure are solved using the Newmark step-by-step integration procedure in the time domain allowing the stresses and displacement to be computed. After each time step the tangent shear and bulk modulus are re-evaluated. Hysteretic damping as a result of the hyperbolic shear stress-strain law is inherent in the model. Viscous damping may also be included. The analysis is applied to a number of dams and slopes and the earthquake induced displacements are compared with those predicted by a simpler Newmark single degree of freedom rigid plastic analysis. As well, a comparison is made with Makdisi's prediction of deformation of embankments. For a clay slope structure, the overall displacements are of similar order. For a clay dam struture the non-linear finite element results indicate that the Newmark type methods are overly conservative. The more rigorous multi-degree of freedom analysis allows the distribution of displacements within and on the surface of the embankment to be obtained.

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