Verification and numerical implementation of a 3D liquefaction model

Abstract

With the advancement of solution techniques and solving computers, 3D analysis of civil engineering problems has increasingly become more interesting. The multiple spring model is one of the tools to give good solutions to 3D liquefaction analyses. In this model, the deviatoric stress is determined in a finite number of springs distributed over virtual planes in the soil element for which liquefaction analysis is to be undergone. Among the several options for the distribution of the virtual planes in the soil element, it was previously found that an icosahedral distribution results in an isotropic model. For the displacement based analysis which is going to be discussed in this report, the global strains will be decomposed into one-dimensional strains in each spring through transformation matrices. Then the Masing rule after several modifications will be used to obtain stress ratio from those transformed strains. The product of the stress ratio and the mean effective stress gives the shear stress in each spring. The global shear stress of the soil mass is calculated from the shear stress in each spring through transformation matrices. The model also uses stress-dilatancy relationships to calculate volumetric strain due to dilatancy which enables to calculate the volumetric strain due to consolidation. Expressions for a curve of isotropic compression or swelling help to calculate the mean effective stress. Along with the stress ratio, it is this mean effective stress that will be used to calculate the shear stress in each spring. In this report, it is discovered that the icosahedral distribution of planes results in an isotropic behavior. However, the way the springs are oriented on those plane as described in the original model by Nishimura (2002) will not result in an isotropic behavior. At the end of the report, suggestions will be given to overcome this anisotropy. It will also be seen that the volumetric strain due to dilatancy is overestimated in the model. The source for the overestimation is discovered and will be forwarded for further improvement. Suggestions for the modification of the hysteresis loop when the stress ratio in the past is exceeded will also be given.